├── .gitignore ├── README.md ├── bin ├── gen-sha └── sanitize └── cute ├── 3pk.mod ├── SHASUM ├── aircrfta.mod ├── aircrftb.mod ├── airport.mod ├── aljazzaf.mod ├── allinit.mod ├── allinitc.mod ├── allinitu.mod ├── alsotame.mod ├── argauss.mod ├── arglina.mod ├── arglinb.mod ├── arglinc.mod ├── argtrig.mod ├── artif.mod ├── arwhead.mod ├── aug2d.mod ├── aug2dc.mod ├── aug2dcqp.mod ├── aug2dqp.mod ├── aug3d.mod ├── aug3dc.mod ├── aug3dcqp.mod ├── aug3dqp.mod ├── avgasa.mod ├── avgasb.mod ├── avion2.mod ├── bard.mod ├── batch.mod ├── bdexp.mod ├── bdqrtic.mod ├── bdvalue.mod ├── beale.mod ├── bigbank.mod ├── biggs3.mod ├── biggs5.mod ├── biggs6.mod ├── biggsb1.mod ├── biggsc4.mod ├── blockqp1.mod ├── blockqp2.mod ├── blockqp3.mod ├── blockqp4.mod ├── blockqp5.mod ├── bloweya.mod ├── bloweyb.mod ├── bloweyc.mod ├── booth.mod ├── box2.mod ├── box3.mod ├── bqp1var.mod ├── bqpgabim.mod ├── bqpgasim.mod ├── brainpc0.mod ├── brainpc1.mod ├── brainpc2.mod ├── brainpc3.mod ├── brainpc4.mod ├── brainpc5.mod ├── brainpc6.mod ├── brainpc7.mod ├── brainpc8.mod ├── brainpc9.mod ├── bratu1d.mod ├── bratu2d.mod ├── bratu2dt.mod ├── bratu3d.mod ├── britgas.mod ├── brkmcc.mod ├── brownal.mod ├── brownbs.mod ├── brownden.mod ├── broydn3d.mod ├── broydn7d.mod ├── broydnbd.mod ├── brybnd.mod ├── bt1.mod ├── bt10.mod ├── bt11.mod ├── bt12.mod ├── bt13.mod ├── bt2.mod ├── bt3.mod ├── bt4.mod ├── bt5.mod ├── bt6.mod ├── bt7.mod ├── bt8.mod ├── bt9.mod ├── byrdsphr.mod ├── camel6.mod ├── cantilvr.mod ├── catena.mod ├── catenary.mod ├── cb2.mod ├── cb3.mod ├── cbratu2d.mod ├── cbratu3d.mod ├── chaconn1.mod ├── chaconn2.mod ├── chainwoo.mod ├── chandheq.mod ├── chebyqad.mod ├── chemrcta.mod ├── chemrctb.mod ├── chenhark.mod ├── chnrosnb.mod ├── cliff.mod ├── clnlbeam.mod ├── clplatea.mod ├── clplateb.mod ├── clplatec.mod ├── cluster.mod ├── concon.mod ├── congigmz.mod ├── coolhans.mod ├── core1.mod ├── core2.mod ├── corkscrw.mod ├── coshfun.mod ├── cosine.mod ├── cragglvy.mod ├── cresc100.mod ├── cresc132.mod ├── cresc4.mod ├── cresc50.mod ├── csfi1.mod ├── csfi2.mod ├── cube.mod ├── curly10.mod ├── curly20.mod ├── curly30.mod ├── cvxbqp1.mod ├── cvxqp1.mod ├── cvxqp2.mod ├── cvxqp3.mod ├── dallasl.mod ├── dallasm.mod ├── dallass.mod ├── deconvb.mod ├── deconvc.mod ├── deconvu.mod ├── degenlpa.mod ├── degenlpb.mod ├── demymalo.mod ├── denschna.mod ├── denschnb.mod ├── denschnc.mod ├── denschnd.mod ├── denschne.mod ├── denschnf.mod ├── dipigri.mod ├── disc2.mod ├── discs.mod ├── dittert.mod ├── dixchlng.mod ├── dixchlnv.mod ├── dixmaana.mod ├── dixmaanb.mod ├── dixmaanc.mod ├── dixmaand.mod ├── dixmaane.mod ├── dixmaanf.mod ├── dixmaang.mod ├── dixmaanh.mod ├── dixmaani.mod ├── dixmaanj.mod ├── dixmaank.mod ├── dixmaanl.mod ├── dixon3dq.mod ├── djtl.mod ├── dnieper.mod ├── dqdrtic.mod ├── dqrtic.mod ├── drcav1lq.mod ├── drcav2lq.mod ├── drcav3lq.mod ├── drcavty1.mod ├── drcavty2.mod ├── drcavty3.mod ├── dtoc1l.mod ├── dtoc1na.mod ├── dtoc1nb.mod ├── dtoc1nc.mod ├── dtoc1nd.mod ├── dtoc2.mod ├── dtoc3.mod ├── dtoc4.mod ├── dtoc5.mod ├── dtoc6.mod ├── dual1.mod ├── dual2.mod ├── dual3.mod ├── dual4.mod ├── dualc1.mod ├── dualc2.mod ├── dualc5.mod ├── dualc8.mod ├── edensch.mod ├── eg1.mod ├── eg2.mod ├── eg3.mod ├── eigena.mod ├── eigena2.mod ├── eigenaco.mod ├── eigenals.mod ├── eigenb.mod ├── eigenb2.mod ├── eigenbco.mod ├── eigenbls.mod ├── eigenc2.mod ├── eigencco.mod ├── eigmaxa.mod ├── eigmaxb.mod ├── eigmaxc.mod ├── eigmina.mod ├── eigminb.mod ├── eigminc.mod ├── engval1.mod ├── engval2.mod ├── errinros.mod ├── expfit.mod ├── expfita.mod ├── expfitb.mod ├── expfitc.mod ├── explin.mod ├── explin2.mod ├── expquad.mod ├── extrasim.mod ├── extrosnb.mod ├── fccu.mod ├── fletcbv2.mod ├── fletcbv3.mod ├── fletchbv.mod ├── fletchcr.mod ├── fletcher.mod ├── flosp2hh.mod ├── flosp2hl.mod ├── flosp2hm.mod ├── flosp2th.mod ├── flosp2tl.mod ├── flosp2tm.mod ├── fminsrf2.mod ├── fminsurf.mod ├── freuroth.mod ├── gausselm.mod ├── genhs28.mod ├── genhumps.mod ├── genrose.mod ├── gigomez1.mod ├── gilbert.mod ├── goffin.mod ├── gottfr.mod ├── gouldqp2.mod ├── gouldqp3.mod ├── gpp.mod ├── gridneta.mod ├── gridnetb.mod ├── gridnetc.mod ├── gridnetd.mod ├── gridnete.mod ├── gridnetf.mod ├── gridnetg.mod ├── gridneth.mod ├── gridneti.mod ├── grouping.mod ├── growth.mod ├── growthls.mod ├── gulf.mod ├── hadamals.mod ├── hadamard.mod ├── hager1.mod ├── hager2.mod ├── hager3.mod ├── hager4.mod ├── haifam.mod ├── haifas.mod ├── hairy.mod ├── haldmads.mod ├── hanging.mod ├── harkerp2.mod ├── hart6.mod ├── hatflda.mod ├── hatfldb.mod ├── hatfldc.mod ├── hatfldd.mod ├── hatflde.mod ├── hatfldf.mod ├── hatfldg.mod ├── hatfldh.mod ├── heart6.mod ├── heart6ls.mod ├── heart8.mod ├── heart8ls.mod ├── helix.mod ├── hilberta.mod ├── hilbertb.mod ├── himmelba.mod ├── himmelbb.mod ├── himmelbc.mod ├── himmelbd.mod ├── himmelbe.mod ├── himmelbf.mod ├── himmelbg.mod ├── himmelbh.mod ├── himmelbi.mod ├── himmelbj.mod ├── himmelbk.mod ├── himmelp1.mod ├── himmelp2.mod ├── himmelp3.mod ├── himmelp4.mod ├── himmelp5.mod ├── himmelp6.mod ├── hong.mod ├── hs001.mod ├── hs002.mod ├── hs003.mod ├── hs004.mod ├── hs005.mod ├── hs006.mod ├── hs007.mod ├── hs008.mod ├── hs009.mod ├── hs010.mod ├── hs011.mod ├── hs012.mod ├── hs013.mod ├── hs014.mod ├── hs015.mod ├── hs016.mod ├── hs017.mod ├── hs018.mod ├── hs019.mod ├── hs020.mod ├── hs021.mod ├── hs022.mod ├── hs023.mod ├── hs024.mod ├── hs025.mod ├── hs026.mod ├── hs027.mod ├── hs028.mod ├── hs029.mod ├── hs030.mod ├── hs031.mod ├── hs032.mod ├── hs033.mod ├── hs034.mod ├── hs035.mod ├── hs036.mod ├── hs037.mod ├── hs038.mod ├── hs039.mod ├── hs040.mod ├── hs041.mod ├── hs042.mod ├── hs043.mod ├── hs044.mod ├── hs045.mod ├── hs046.mod ├── hs047.mod ├── hs048.mod ├── hs049.mod ├── hs050.mod ├── hs051.mod ├── hs052.mod ├── hs053.mod ├── hs054.mod ├── hs055.mod ├── hs056.mod ├── hs057.mod ├── hs059.mod ├── hs060.mod ├── hs061.mod ├── hs062.mod ├── hs063.mod ├── hs064.mod ├── hs065.mod ├── hs066.mod ├── hs067.mod ├── hs068.mod ├── hs069.mod ├── hs070.mod ├── hs071.mod ├── hs072.mod ├── hs073.mod ├── hs074.mod ├── hs075.mod ├── hs076.mod ├── hs077.mod ├── hs078.mod ├── hs079.mod ├── hs080.mod ├── hs081.mod ├── hs083.mod ├── hs084.mod ├── hs085.mod ├── hs086.mod ├── hs087.mod ├── hs088.mod ├── hs089.mod ├── hs090.mod ├── hs091.mod ├── hs092.mod ├── hs093.mod ├── hs095.mod ├── hs096.mod ├── hs097.mod ├── hs098.mod ├── hs099.mod ├── hs100.mod ├── hs100lnp.mod ├── hs100mod.mod ├── hs101.mod ├── hs102.mod ├── hs103.mod ├── hs104.mod ├── hs105.mod ├── hs106.mod ├── hs107.mod ├── hs108.mod ├── hs109.mod ├── hs110.mod ├── hs111.mod ├── hs111lnp.mod ├── hs112.mod ├── hs113.mod ├── hs114.mod ├── hs116.mod ├── hs117.mod ├── hs118.mod ├── hs119.mod ├── hs21mod.mod ├── hs268.mod ├── hs35mod.mod ├── hs3mod.mod ├── hs44new.mod ├── hs99exp.mod ├── hubfit.mod ├── hues-mod.mod ├── huestis.mod ├── humps.mod ├── hvycrash.mod ├── hypcir.mod ├── indef.mod ├── integreq.mod ├── jensmp.mod ├── kissing.mod ├── kiwcresc.mod ├── kowosb.mod ├── ksip.mod ├── lakes.mod ├── launch.mod ├── lch.mod ├── lewispol.mod ├── liarwhd.mod ├── linspanh.mod ├── liswet1.mod ├── liswet10.mod ├── liswet11.mod ├── liswet12.mod ├── liswet2.mod ├── liswet3.mod ├── liswet4.mod ├── liswet5.mod ├── liswet6.mod ├── liswet7.mod ├── liswet8.mod ├── liswet9.mod ├── lminsurf.mod ├── loadbal.mod ├── loghairy.mod ├── logros.mod ├── lootsma.mod ├── lotschd.mod ├── lsnnodoc.mod ├── lsqfit.mod ├── madsen.mod ├── madsschj.mod ├── makela1.mod ├── makela2.mod ├── makela3.mod ├── makela4.mod ├── mancino.mod ├── manne.mod ├── maratos.mod ├── maratosb.mod ├── matrix2.mod ├── maxlika.mod ├── mccormck.mod ├── mconcon.mod ├── mdhole.mod ├── methanb8.mod ├── methanl8.mod ├── mexhat.mod ├── meyer3.mod ├── mifflin1.mod ├── mifflin2.mod ├── minc44.mod ├── minmaxbd.mod ├── minmaxrb.mod ├── minperm.mod ├── minsurf.mod ├── mistake.mod ├── model.mod ├── morebv.mod ├── mosarqp1.mod ├── mosarqp2.mod ├── msqrta.mod ├── msqrtals.mod ├── msqrtb.mod ├── msqrtbls.mod ├── mwright.mod ├── nasty.mod ├── ncvxbqp1.mod ├── ncvxbqp2.mod ├── ncvxbqp3.mod ├── ncvxqp1.mod ├── ncvxqp2.mod ├── ncvxqp3.mod ├── ncvxqp4.mod ├── ncvxqp5.mod ├── ncvxqp6.mod ├── ncvxqp7.mod ├── ncvxqp8.mod ├── ncvxqp9.mod ├── ngone.mod ├── noncvxu2.mod ├── noncvxun.mod ├── nondia.mod ├── nondquar.mod ├── nonmsqrt.mod ├── nonscomp.mod ├── nuffield.mod ├── nuffield2.mod ├── nuffield2_trap.mod ├── nuffield_continuum.mod ├── obstclal.mod ├── obstclbl.mod ├── obstclbu.mod ├── odfits.mod ├── oet1.mod ├── oet2.mod ├── oet3.mod ├── oet7.mod ├── optcdeg2.mod ├── optcdeg3.mod ├── optcntrl.mod ├── optctrl3.mod ├── optctrl6.mod ├── optmass.mod ├── optprloc.mod ├── orthrdm2.mod ├── orthrds2.mod ├── orthrega.mod ├── orthregb.mod ├── orthregc.mod ├── orthregd.mod ├── orthrege.mod ├── orthrgdm.mod ├── orthrgds.mod ├── osbornea.mod ├── osborneb.mod ├── oslbqp.mod ├── palmer1.mod ├── palmer1a.mod ├── palmer1b.mod ├── palmer1c.mod ├── palmer1d.mod ├── palmer1e.mod ├── palmer2.mod ├── palmer2a.mod ├── palmer2b.mod ├── palmer2c.mod ├── palmer2e.mod ├── palmer3.mod ├── palmer3a.mod ├── palmer3b.mod ├── palmer3c.mod ├── palmer3e.mod ├── palmer4.mod ├── palmer4a.mod ├── palmer4b.mod ├── palmer4c.mod ├── palmer4e.mod ├── palmer5a.mod ├── palmer5b.mod ├── palmer5c.mod ├── palmer5d.mod ├── palmer5e.mod ├── palmer6a.mod ├── palmer6c.mod ├── palmer6e.mod ├── palmer7a.mod ├── palmer7c.mod ├── palmer7e.mod ├── palmer8a.mod ├── palmer8c.mod ├── palmer8e.mod ├── penalty1.mod ├── penalty2.mod ├── pentagon.mod ├── pentdi.mod ├── pfit1.mod ├── pfit1ls.mod ├── pfit2.mod ├── pfit2ls.mod ├── pfit3.mod ├── pfit3ls.mod ├── pfit4.mod ├── pfit4ls.mod ├── polak1.mod ├── polak2.mod ├── polak3.mod ├── polak4.mod ├── polak5.mod ├── polak6.mod ├── porous1.mod ├── porous2.mod ├── portfl1.mod ├── portfl2.mod ├── portfl3.mod ├── portfl4.mod ├── portfl6.mod ├── powell20.mod ├── powellbs.mod ├── powellsq.mod ├── power.mod ├── probpenl.mod ├── prodpl0.mod ├── prodpl1.mod ├── pspdoc.mod ├── pt.mod ├── qpcboei1.mod ├── qpcboei2.mod ├── qpcstair.mod ├── qpnboei1.mod ├── qpnboei2.mod ├── qpnstair.mod ├── qr3d.mod ├── qr3dbd.mod ├── qr3dls.mod ├── qrtquad.mod ├── quartc.mod ├── qudlin.mod ├── reading1.mod ├── reading2.mod ├── reading3.mod ├── recipe.mod ├── res.mod ├── rk23.mod ├── robot.mod ├── rosenbr.mod ├── rosenmmx.mod ├── s332.mod ├── s365mod.mod ├── s368.mod ├── sawpath.mod ├── scon1dls.mod ├── scosine.mod ├── scurly10.mod ├── scurly20.mod ├── scurly30.mod ├── semicon1.mod ├── semicon2.mod ├── sensors.mod ├── sim2bqp.mod ├── simbqp.mod ├── simpllpa.mod ├── simpllpb.mod ├── sineali.mod ├── sineval.mod ├── sinquad.mod ├── sinrosnb.mod ├── sipow1.mod ├── sipow1m.mod ├── sipow2.mod ├── sipow2m.mod ├── sipow3.mod ├── sipow4.mod ├── sisser.mod ├── smbank.mod ├── smmpsf.mod ├── snake.mod ├── sosqp1.mod ├── sosqp2.mod ├── spanhyd.mod ├── spiral.mod ├── sreadin3.mod ├── srosenbr.mod ├── sseblin.mod ├── ssebnln.mod ├── ssnlbeam.mod ├── stancmin.mod ├── static3.mod ├── steenbra.mod ├── steenbrb.mod ├── steenbrc.mod ├── steenbrd.mod ├── steenbre.mod ├── steenbrf.mod ├── steenbrg.mod ├── supersim.mod ├── svanberg.mod ├── swopf.mod ├── synthes1.mod ├── tame.mod ├── tfi2.mod ├── tointqor.mod ├── trainf.mod ├── trainh.mod ├── tridia.mod ├── trimloss.mod ├── try-b.mod ├── twirism1.mod ├── twobars.mod ├── ubh1.mod ├── ubh5.mod ├── vanderm1.mod ├── vanderm2.mod ├── vanderm3.mod ├── vanderm4.mod ├── vardim.mod ├── watson.mod ├── weeds.mod ├── womflet.mod ├── woods.mod ├── yao.mod ├── yfit.mod ├── yfitu.mod ├── zangwil2.mod ├── zangwil3.mod ├── zecevic2.mod ├── zecevic3.mod ├── zecevic4.mod ├── zigzag.mod └── zy2.mod /.gitignore: -------------------------------------------------------------------------------- 1 | *~ 2 | *.nl 3 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | This is a repository of optimization test problems. 2 | 3 | The AMPL problems were obtained from Robert Vanderbei's webpage: 4 | 5 | http://www.orfe.princeton.edu/~rvdb/ampl/nlmodels/ 6 | 7 | and many were created or translated by Hande Yurttan. 8 | 9 | Each problem set has a file SHASUM with checksums of each test 10 | problem. These checksums can be used to verify the integrity of the 11 | test problems. This file is created with the command 12 | 13 | shasum *.mod | awk '{printf("%-25s %s\n", $2, $1);}' > SHASUM 14 | 15 | Changelog: 16 | 23 Mar 2011: Initial checkin, cute problems only. 17 | -------------------------------------------------------------------------------- /bin/gen-sha: -------------------------------------------------------------------------------- 1 | #!/bin/sh 2 | shasum *.mod | awk '{printf("%-25s %s\n", $2, $1);}' 3 | -------------------------------------------------------------------------------- /bin/sanitize: -------------------------------------------------------------------------------- 1 | #!/bin/bash 2 | # Sanitize the problems. Use via the command 3 | # ls *.mod | sanitize 4 | 5 | while read problem 6 | do 7 | echo "sanitizing $problem" 8 | # remove solve/display/options commands and trailing space/tab 9 | sed \ 10 | -e 's/solve\;//g' \ 11 | -e 's/display[^;]*\;//g' \ 12 | -e 's/option[^;]*\;//g' \ 13 | -e 's/[ ]*$//' \ 14 | ${problem} > ${problem}.new 15 | # remove trailing new lines 16 | sed \ 17 | -e :a -e '/^\n*$/{$d;N;ba' -e '}' \ 18 | ${problem}.new > ${problem} 19 | rm -f ${problem}.new 20 | done 21 | -------------------------------------------------------------------------------- /cute/allinitu.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # N. Gould, private communication. 14 | 15 | # SIF input: Nick Gould, June 1990. 16 | 17 | # classification OUR2-AY-4-0 18 | 19 | var x{1..4}; 20 | 21 | minimize f: 22 | x[3]-1 + 23 | x[1]^2+ 24 | x[2]^2 + (x[3]+x[4])^2 + 25 | sin(x[3])^2 + x[1]^2*x[2]^2 + x[4]-3 + 26 | sin(x[3])^2 + 27 | (x[4]-1)^2 + 28 | (x[2]^2)^2+ 29 | (x[3]^2 + (x[4]+x[1])^2)^2 + 30 | (x[1]-4 + sin(x[4])^2 + x[2]^2*x[3]^2)^2 + 31 | sin(x[4])^4; 32 | -------------------------------------------------------------------------------- /cute/alsotame.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # A.R. Conn, N. Gould and Ph.L. Toint, 14 | # "The LANCELOT User's Manual", 15 | # Dept of Maths, FUNDP, 1991. 16 | 17 | # SIF input: Ph. Toint, Jan 1991. 18 | 19 | # classification OOR2-AN-2-1 20 | 21 | var x; 22 | var y; 23 | 24 | minimize f: 25 | exp(x-2*y); 26 | 27 | subject to cons1: 28 | sin(-x+y-1)=0; 29 | subject to cons2: 30 | -2 <= x <= 2; 31 | subject to cons3: 32 | -1.5 <= y <= 1.5; 33 | -------------------------------------------------------------------------------- /cute/arglinb.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: Problem 33 in 13 | # J.J. More', B.S. Garbow and K.E. Hillstrom, 14 | # "Testing Unconstrained Optimization Software", 15 | # ACM Transactions on Mathematical Software, vol. 7(1), pp. 17-41, 1981. 16 | 17 | # See also Buckley#93 (with different N and M) 18 | # SIF input: Ph. Toint, Dec 1989. 19 | 20 | # classification SUR2-AN-V-0 21 | 22 | param N:=10; 23 | param M:=20; 24 | var x{1..N}:=1.0; 25 | minimize f: 26 | sum {i in 1..M} ( sum {j in 1..N} x[j]*i*j -1.0)^2; 27 | -------------------------------------------------------------------------------- /cute/arglinc.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: Problem 34 in 13 | # J.J. More', B.S. Garbow and K.E. Hillstrom, 14 | # "Testing Unconstrained Optimization Software", 15 | # ACM Transactions on Mathematical Software, vol. 7(1), pp. 17-41, 1981. 16 | 17 | # See also Buckley#101 (with different N and M) 18 | # SIF input: Ph. Toint, Dec 1989. 19 | 20 | # classification SUR2-AN-V-0 21 | 22 | param N:=10; 23 | param M:=20; 24 | var x{1..N} := 1.0; 25 | 26 | minimize f: 27 | 2 + sum {i in 2..M-1} (sum {j in 2..N-1} x[j]*j*(i-1) - 1.0)^2; 28 | -------------------------------------------------------------------------------- /cute/argtrig.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: Problem 26 in 13 | # J.J. More', B.S. Garbow and K.E. Hillstrom, 14 | # "Testing Unconstrained Optimization Software", 15 | # ACM Transactions on Mathematical Software, vol. 7(1), pp. 17-41, 1981. 16 | 17 | # SIF input: Ph. Toint, Dec 1989. 18 | 19 | # classification NOR2-AN-V-V 20 | 21 | param N:=100; 22 | var x{1..N} := 1/N; 23 | 24 | minimize f: 0; 25 | subject to cons{i in 1..N}: 26 | (i*(cos(x[i])+sin(x[i])) + sum {j in 1..N} cos(x[j]) - (N+i) ) = 0; 27 | -------------------------------------------------------------------------------- /cute/arwhead.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: Problem 55 in 13 | # A.R. Conn, N.I.M. Gould, M. Lescrenier and Ph.L. Toint, 14 | # "Performance of a multifrontal scheme for partially separable 15 | # optimization", 16 | # Report 88/4, Dept of Mathematics, FUNDP (Namur, B), 1988. 17 | 18 | # SIF input: Ph. Toint, Dec 1989. 19 | 20 | # classification OUR2-AN-V-0 21 | 22 | param N:=5000; 23 | var x{1..N} := 1.0; 24 | 25 | minimize f: 26 | sum {i in 1..N-1} (-4*x[i]+3.0) + sum {i in 1..N-1} (x[i]^2+x[N]^2)^2; 27 | -------------------------------------------------------------------------------- /cute/bdexp.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: Problem 56 in 13 | # A.R. Conn, N.I.M. Gould, M. Lescrenier and Ph.L. Toint, 14 | # "Performance of a multifrontal scheme for partially separable 15 | # optimization", 16 | # Report 88/4, Dept of Mathematics, FUNDP (Namur, B), 1988. 17 | 18 | # SIF input: Ph. Toint, Dec 1989. 19 | 20 | # classification OBR2-AY-V-0 21 | 22 | param N := 5000; 23 | param ngs := N-2; 24 | var x{1..N} := 1.0; 25 | 26 | minimize f: 27 | sum {i in 1..ngs} (x[i]+x[i+1])*exp((x[i]+x[i+1])*(-x[i+2])); 28 | -------------------------------------------------------------------------------- /cute/bdqrtic.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: Problem 61 in 13 | # A.R. Conn, N.I.M. Gould, M. Lescrenier and Ph.L. Toint, 14 | # "Performance of a multifrontal scheme for partially separable 15 | # optimization", 16 | # Report 88/4, Dept of Mathematics, FUNDP (Namur, B), 1988. 17 | 18 | # SIF input: Ph. Toint, Dec 1989. 19 | 20 | # classification SUR2-AN-V-0 21 | 22 | param N:=1000; 23 | var x{1..N} := 1.0; 24 | 25 | minimize f: 26 | sum {i in 1..N-4} (-4*x[i]+3.0)^2 + sum {i in 1..N-4} (x[i]^2+2*x[i+1]^2+3*x[i+2]^2+4*x[i+3]^2+5*x[N]^2)^2; 27 | -------------------------------------------------------------------------------- /cute/beale.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: Problem 5 in 13 | # J.J. More', B.S. Garbow and K.E. Hillstrom, 14 | # "Testing Unconstrained Optimization Software", 15 | # ACM Transactions on Mathematical Software, vol. 7(1), pp. 17-41, 1981. 16 | 17 | # See also Buckley#89. 18 | # SIF input: Ph. Toint, Dec 1989. 19 | 20 | # classification SUR2-AN-2-0 21 | 22 | param N:=2; 23 | var x{1..N} := 1.0; 24 | 25 | minimize f: 26 | (-1.5+x[1]*(1.0-x[2]))^2 + (-2.25+x[1]*(1.0-x[2]^2))^2 + (-2.625+x[1]*(1.0-x[2]^3))^2; 27 | -------------------------------------------------------------------------------- /cute/biggsb1.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # M. Batholomew-Biggs and F.G. Hernandez, 14 | # "Some improvements to the subroutine OPALQP for dealing with large 15 | # problems", 16 | # Numerical Optimization Centre, Hatfield, 1992. 17 | 18 | # SIF input: Ph Toint, April 1992. 19 | 20 | # classification QBR2-AN-V-V 21 | 22 | param N := 1000; 23 | var x{i in 1..N}; 24 | 25 | minimize f: 26 | (x[1]-1)^2 + sum {i in 1..N-1} (x[i+1]-x[i])^2 + (1-x[N])^2; 27 | 28 | subject to cons1{i in 1..N-1}: 29 | 0.0 <= x[i] <= 0.9; 30 | -------------------------------------------------------------------------------- /cute/blockqp1.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification QLR2-AN-V-V 13 | 14 | param n := 1000; 15 | param b := 5; 16 | var x{1..n} >= -1, <= 1, := 0.99; 17 | var y{1..n} >= -1, <= 1, := -0.99; 18 | var z{1..b} >= 0, <= 2, := 0.5; 19 | 20 | minimize f: 21 | sum {i in 1..n} x[i]*y[i] + sum {j in 1..b} 0.5*z[j]^2 22 | ; 23 | 24 | subject to cons1: 25 | sum {i in 1..n} (x[i] + y[i]) + sum {j in 1..b} z[j] >= b+1; 26 | subject to cons2{i in 1..n}: 27 | x[i] + y[i] + sum {j in 1..b} z[j] = b; 28 | -------------------------------------------------------------------------------- /cute/blockqp2.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification QLR2-AN-V-V 13 | 14 | param n := 1000; 15 | param b := 5; 16 | var x{1..n} >= -1, <= 1, := 0.99; 17 | var y{1..n} >= -1, <= 1, := -0.99; 18 | var z{1..b} >= 0, <= 2, := 0.5; 19 | 20 | minimize f: 21 | sum {i in 1..n} x[i]*y[i] + sum {j in 1..b} 0.5*z[j]^2 22 | ; 23 | 24 | subject to cons1: 25 | sum {i in 1..n} (x[i] + y[i]) + sum {j in 1..b} z[j] >= b+1; 26 | subject to cons2{i in 1..n}: 27 | x[i] - y[i] + sum {j in 1..b} z[j] = b; 28 | -------------------------------------------------------------------------------- /cute/blockqp3.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification QLR2-AN-V-V 13 | 14 | param n := 1000; 15 | param b := 5; 16 | var x{1..n} >= -1, <= 1, := 0.99; 17 | var y{1..n} >= -1, <= 1, := -0.99; 18 | var z{1..b} >= 0, <= 2, := 0.5; 19 | 20 | minimize f: 21 | sum {i in 1..n} (i/n)*(x[i]*y[i]) + sum {j in 1..b} 0.5*z[j]^2 22 | ; 23 | 24 | subject to cons1: 25 | sum {i in 1..n} (x[i] + y[i]) + sum {j in 1..b} z[j] >= b+1; 26 | subject to cons2{i in 1..n}: 27 | x[i] + y[i] + sum {j in 1..b} z[j] = b; 28 | -------------------------------------------------------------------------------- /cute/blockqp4.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification QLR2-AN-V-V 13 | 14 | param n := 1000; 15 | param b := 5; 16 | var x{1..n} >= -1, <= 1, := 0.99; 17 | var y{1..n} >= -1, <= 1, := -0.99; 18 | var z{1..b} >= 0, <= 2, := 0.5; 19 | 20 | minimize f: 21 | sum {i in 1..n} (i/n)*(x[i]*y[i]) + sum {j in 1..b} 0.5*z[j]^2 22 | ; 23 | 24 | subject to cons1: 25 | sum {i in 1..n} (x[i] + y[i]) + sum {j in 1..b} z[j] >= b+1; 26 | subject to cons2{i in 1..n}: 27 | x[i] - y[i] + sum {j in 1..b} z[j] = b; 28 | -------------------------------------------------------------------------------- /cute/blockqp5.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification QLR2-AN-V-V 13 | 14 | param n := 1000; 15 | param b := 5; 16 | var x{1..n} >= -1, <= 1, := 0.99; 17 | var y{1..n} >= -1, <= 1, := -0.99; 18 | var z{1..b} >= 0, <= 1, := 0.5; 19 | 20 | minimize f: 21 | sum {i in 1..n} (i/n)*(x[i]*y[i]) + sum {j in 1..b} 0.5*z[j]^2 22 | ; 23 | 24 | subject to cons1: 25 | sum {i in 1..n} (x[i] + y[i]) + sum {j in 1..b} z[j] >= b+1; 26 | subject to cons2{i in 1..n}: 27 | x[i] + y[i] + sum {j in 1..b} z[j] = b; 28 | -------------------------------------------------------------------------------- /cute/booth.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: Problem 36 in 13 | # A.R. Buckley, 14 | # "Test functions for unconstrained minimization", 15 | # TR 1989CS-3, Mathematics, statistics and computing centre, 16 | # Dalhousie University, Halifax (CDN), 1989. 17 | 18 | # SIF input: Ph. Toint, Dec 1989. 19 | 20 | # classification NLR2-AN-2-2 21 | 22 | var x{1..2}; 23 | 24 | minimize f: 0; 25 | subject to cons1: 26 | (x[1]+2*x[2]-7) = 0; 27 | subject to cons2: 28 | (2*x[1]+x[2]-5) = 0; 29 | -------------------------------------------------------------------------------- /cute/bqp1var.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: a one variable box-constrained quadratic 13 | 14 | # SIF input: Nick Gould, March 1992 15 | 16 | # classification QBR2-AN-1-0 17 | 18 | var x1:=0.25; 19 | minimize f: 20 | x1+x1^2; 21 | subject to cons1: 22 | 0.0 <= x1 <= 0.5; 23 | -------------------------------------------------------------------------------- /cute/brkmcc.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: Problem 85 (p.35) in 13 | # A.R. Buckley, 14 | # "Test functions for unconstrained minimization", 15 | # TR 1989CS-3, Mathematics, statistics and computing centre, 16 | # Dalhousie University, Halifax (CDN), 1989. 17 | 18 | # SIF input: Ph. Toint, Dec 1989. 19 | 20 | # classification OUR2-AN-2-0 21 | 22 | var x{1..2} := 2.0; 23 | minimize f: 24 | (x[1]-2)^2 + (x[2]-1)^2 + (1/(1-0.25*x[1]^2-x[2]^2))/25 + 5*(x[1]-2*x[2]+1)^2; 25 | -------------------------------------------------------------------------------- /cute/brownal.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: Problem 27 in 13 | # J.J. More', B.S. Garbow and K.E. Hillstrom, 14 | # "Testing Unconstrained Optimization Software", 15 | # ACM Transactions on Mathematical Software, vol. 7(1), pp. 17-41, 1981. 16 | 17 | # See also Buckley#79 18 | # SIF input: Ph. Toint, Dec 1989. 19 | 20 | # classification SUR2-AN-V-0 21 | 22 | param N := 10; 23 | 24 | var x{1..N} := 1/2; 25 | 26 | minimize f: 27 | sum {i in 1..N-1} (x[i]+sum {j in 1..N} x[j] - (N+1) )^2 + (prod {j in 1..N} x[j] - 1)^2; 28 | -------------------------------------------------------------------------------- /cute/brownbs.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: Problem 4 in 13 | # J.J. More', B.S. Garbow and K.E. Hillstrom, 14 | # "Testing Unconstrained Optimization Software", 15 | # ACM Transactions on Mathematical Software, vol. 7(1), pp. 17-41, 1981. 16 | 17 | # See also Buckley#25 18 | # SIF input: Ph. Toint, Dec 1989. 19 | 20 | # classification SUR2-AN-2-0 21 | 22 | param N; 23 | var x{1..N} := 1.0; 24 | 25 | minimize f: 26 | sum {i in 1..N-1} (x[i] - 1000000.0)^2+ 27 | sum {i in 1..N-1} (x[i+1] - 0.000002)^2+ 28 | sum {i in 1..N-1} (x[i]*x[i+1] - 2.0)^2; 29 | data; 30 | param N:=2; 31 | -------------------------------------------------------------------------------- /cute/bt1.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: problem 1 in 13 | # P.T. Boggs and J.W. Tolle, 14 | # "A strategy for global convergence in a sequential 15 | # quadratic programming algorithm", 16 | # SINUM 26(3), pp. 600-623, 1989. 17 | 18 | # SIF input: Ph. Toint, June 1993. 19 | 20 | # classification QQR2-AN-2-1 21 | 22 | var x{1..2}; 23 | minimize f: 24 | 100*x[1]^2+100*x[2]^2-x[1]-100; 25 | subject to cons1: 26 | x[1]^2+x[2]^2-1.0=0; 27 | 28 | data; 29 | let x[1] := 0.08; 30 | let x[2] := 0.06; 31 | -------------------------------------------------------------------------------- /cute/bt2.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: problem 2 in 13 | # P.T. Boggs and J.W. Tolle, 14 | # "A strategy for global convergence in a sequential 15 | # quadratic programming algorithm", 16 | # SINUM 26(3), pp. 600-623, 1989. 17 | 18 | # SIF input: Ph. Toint, June 1993. 19 | 20 | # classification QQR2-AY-3-1 21 | 22 | var x{1..3} := 10.0; 23 | 24 | minimize f: 25 | (x[1]-1.0)^2 + (x[1]-x[2])^2 + (x[2]-x[3])^4; 26 | subject to cons1: 27 | x[1]*(1.0+x[2]^2)+x[3]^4 = 8.2426407; 28 | -------------------------------------------------------------------------------- /cute/bt8.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: problem 8 in 13 | # P.T. Boggs and J.W. Tolle, 14 | # "A strategy for global convergence in a sequential 15 | # quadratic programming algorithm", 16 | # SINUM 26(3), pp. 600-623, 1989. 17 | 18 | # The problem is not convex. 19 | 20 | # SIF input: Ph. Toint, June 1993. 21 | 22 | # classification QQR2-AN-5-2 23 | 24 | var x{i in 1..5} := if (i <= 3) then 1.0 else 0.0; 25 | 26 | minimize f: 27 | x[1]^2+x[2]^2+x[3]^2; 28 | subject to cons1: 29 | x[1]-1-x[4]^2+x[2]^2 = 0; 30 | subject to cons2: 31 | -1+x[1]^2+x[2]^2-x[5]^2 = 0; 32 | -------------------------------------------------------------------------------- /cute/byrdsphr.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # R. Byrd, 14 | # Private communication, Chicago, 1992. 15 | 16 | # SIF input: Ph. Toint, November 1992. 17 | 18 | # classification LQR2-AN-3-2 19 | 20 | param xinit{1..3}; 21 | var x{i in 1..3} := xinit[i]; 22 | 23 | minimize f: 24 | -x[1]-x[2]-x[3]; 25 | subject to cons1: 26 | -9.0+x[1]^2+x[2]^2+x[3]^2 = 0; 27 | subject to cons2: 28 | -9.0+(x[1]-1.0)^2+x[2]^2+x[3]^2 = 0; 29 | 30 | data; 31 | param xinit:= 32 | 1 5.0 33 | 2 0.0001 34 | 3 -0.0001; 35 | -------------------------------------------------------------------------------- /cute/camel6.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: Six hump camel in 13 | # L. C. W. Dixon and G. P. Szego (Eds.) 14 | # Towards Global Optimization 15 | # North Holland, 1975. 16 | 17 | # SIF input: A.R. Conn May 1995 18 | 19 | # classification OBR2-AN-2-0 20 | 21 | var x{1..2} := 1.1; 22 | 23 | minimize f: 24 | 4*x[1]^2-2.1*x[1]^4+x[1]^6/3+x[1]*x[2]-4*x[2]^2+4*x[2]^4; 25 | subject to cons1: 26 | -3 <= x[1] <= 3; 27 | subject to cons2: 28 | -1.5 <= x[2] <= 1.5; 29 | -------------------------------------------------------------------------------- /cute/cantilvr.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # an example in a talk by W.K. Zhang and C. Fleury, LLN, 1994. 14 | 15 | # SIF input: Ph. Toint, November 1994 16 | 17 | # classification LOR2-MN-5-1 18 | 19 | param num{1..5}; 20 | var x{1..5} >= 0.000001, := 1.0; 21 | 22 | minimize f: 23 | 0.0624*sum{i in 1..5} x[i]; 24 | subject to cons1: 25 | sum {i in 1..5} num[i]/x[i]^3 - 1 <= 0; 26 | 27 | data; 28 | param num:= 29 | 1 61.0 30 | 2 37.0 31 | 3 19.0 32 | 4 7.0 33 | 5 1.0; 34 | -------------------------------------------------------------------------------- /cute/cb2.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # R. Wommersley and R. Fletcher, 14 | # "An algorithm for composite nonsmooth optimization problems" 15 | # JOTA, vol.48, pp.493-523, 1986 16 | 17 | # SIF input: Ph. Toint, April 1992. 18 | 19 | # classification LOR2-AN-3-3 20 | 21 | var x{1..2} := 2.0; 22 | var u := 1.0; 23 | 24 | minimize f: 25 | u; 26 | subject to cons1: 27 | u-x[1]^2-x[2]^4 >= 0; 28 | subject to cons2: 29 | u-(2.0-x[1])^2-(2.0-x[2])^2 >= 0; 30 | subject to cons3: 31 | u-2*exp(x[2]-x[1]) >= 0; 32 | -------------------------------------------------------------------------------- /cute/cb3.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # R. Wommersley and R. Fletcher, 14 | # "An algorithm for composite nonsmooth optimization problems" 15 | # JOTA, vol.48, pp.493-523, 1986 16 | 17 | # SIF input: Ph. Toint, April 1992. 18 | 19 | # classification LOR2-AN-3-3 20 | 21 | var x{1..2} := 2.0; 22 | var u := 1.0; 23 | 24 | minimize f: 25 | u; 26 | subject to cons1: 27 | u-x[1]^4-x[2]^2 >= 0; 28 | subject to cons2: 29 | u-(2.0-x[1])^2-(2.0-x[2])^2 >= 0; 30 | subject to cons3: 31 | u-2*exp(x[2]-x[1]) >= 0; 32 | -------------------------------------------------------------------------------- /cute/cliff.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: problem 206 (p. 46) in 13 | # A.R. Buckley, 14 | # "Test functions for unconstrained minimization", 15 | # TR 1989CS-3, Mathematics, statistics and computing centre, 16 | # Dalhousie University, Halifax (CDN), 1989. 17 | 18 | # SIF input: Ph. Toint, Dec 1989. 19 | 20 | # classification OUR2-AN-2-0 21 | 22 | param xinit{1..2}; 23 | var x{i in 1..2}:=xinit[i]; 24 | 25 | minimize f: 26 | (0.01*x[1]-0.03)^2 -x[1]+x[2]+exp(20*(x[1]-x[2])); 27 | 28 | data; 29 | param xinit:= 1 0.0 2 -1.0; 30 | -------------------------------------------------------------------------------- /cute/cluster.mod: -------------------------------------------------------------------------------- 1 | # 2 | #************************** 3 | # SET UP THE INITIAL DATA * 4 | #************************** 5 | # Problem : 6 | # ********* 7 | # Source: problem 207 in 8 | # A.R. Buckley, 9 | # "Test functions for unconstrained minimization", 10 | # TR 1989CS-3, Mathematics, statistics and computing centre, 11 | # Dalhousie University, Halifax (CDN), 1989. 12 | # SIF input: Ph. Toint, Dec 1989. 13 | # classification NOR2-AN-2-2 14 | # Solution 15 | 16 | var x1; 17 | var x2; 18 | 19 | minimize obj: 0; 20 | subject to cons1: 21 | ((x1-x2*x2) * (x1-sin(x2))) = 0; 22 | subject to cons2: 23 | (((cos(x2))-x1) * (x2-cos(x1))) = 0; 24 | -------------------------------------------------------------------------------- /cute/cosine.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # N. Gould, private communication. 14 | 15 | # SIF input: N. Gould, Jan 1996 16 | 17 | # classification OUR2-AN-V-0 18 | 19 | param N:=10000; 20 | var x{1..N} := 1.0; 21 | 22 | minimize f: 23 | sum {i in 1..N-1} cos(-0.5*x[i+1]+x[i]^2); 24 | -------------------------------------------------------------------------------- /cute/cube.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: problem 5 (p. 89) in 13 | # A.R. Buckley, 14 | # "Test functions for unconstrained minimization", 15 | # TR 1989CS-3, Mathematics, statistics and computing centre, 16 | # Dalhousie University, Halifax (CDN), 1989. 17 | 18 | # SIF input: Ph. Toint, Dec 1989. 19 | 20 | # classification SUR2-AN-2-0 21 | 22 | param N:=2; 23 | param xinit{1..2}; 24 | var x{i in 1..N} := xinit[i]; 25 | 26 | minimize f: 27 | (x[1]-1.0)^2+sum { i in 2..N} 100*(x[i]-x[i-1]^3)^2; 28 | 29 | data; 30 | param xinit:= 1 -1.2 2 1.0; 31 | -------------------------------------------------------------------------------- /cute/curly10.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: Nick Gould 13 | 14 | # SIF input: Nick Gould, September 1997. 15 | 16 | # classification SUR2-AN-V-0 17 | 18 | param N:=10000; 19 | param K:=10; 20 | 21 | var x{i in 1..N} := 0.0001 * i / (N+1); 22 | var Q{i in 1..N} = if (i <= N-K) then (sum {j in i..i+K} x[j]) else (sum {j in i..N} x[j]); 23 | 24 | minimize f: 25 | sum {i in 1..N} Q[i]*(Q[i]*(Q[i]^2-20)-0.1); 26 | -------------------------------------------------------------------------------- /cute/curly20.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: Nick Gould 13 | 14 | # SIF input: Nick Gould, September 1997. 15 | 16 | # classification SUR2-AN-V-0 17 | 18 | param N:=10000; 19 | param K:=20; 20 | 21 | var x{i in 1..N} := 0.0001 * i / (N+1); 22 | var Q{i in 1..N} = if (i <= N-K) then (sum {j in i..i+K} x[j]) else (sum {j in i..N} x[j]); 23 | 24 | minimize f: 25 | sum {i in 1..N} Q[i]*(Q[i]*(Q[i]^2-20)-0.1); 26 | -------------------------------------------------------------------------------- /cute/curly30.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: Nick Gould 13 | 14 | # SIF input: Nick Gould, September 1997. 15 | 16 | # classification SUR2-AN-V-0 17 | 18 | param N:=10000; 19 | param K:=30; 20 | 21 | var x{i in 1..N} := 0.0001 * i / (N+1); 22 | var Q{i in 1..N} = if (i <= N-K) then (sum {j in i..i+K} x[j]) else (sum {j in i..N} x[j]); 23 | 24 | minimize f: 25 | sum {i in 1..N} Q[i]*(Q[i]*(Q[i]^2-20)-0.1); 26 | -------------------------------------------------------------------------------- /cute/cvxbqp1.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification QBR2-AN-V-0 13 | 14 | param N:=10000; 15 | var x{1..N} >= 0.1, <= 10.0, := 0.5; 16 | 17 | minimize f: 18 | sum {i in 1..N} 0.5*i*(x[i]+x[((2*i-1) mod N)+1]+x[((3*i-1) mod N)+1])^2; 19 | 20 | 21 | # 22 | -------------------------------------------------------------------------------- /cute/cvxqp1.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification QLR2-AN-V-V 13 | 14 | param N:=1000; 15 | param M:=N/2; 16 | 17 | var x{1..N} >= 0.1, <= 10.0, := 0.5; 18 | 19 | minimize f: 20 | sum {i in 1..N} (x[i]+x[((2*i-1) mod N)+1] 21 | +x[((3*i-1) mod N)+1])^2*i/2; 22 | subject to cons1{i in 1..M}: 23 | x[i]+2*x[((4*i-1) mod N)+1] + 3*x[((5*i-1) 24 | mod N)+1] - 6.0 = 0; 25 | -------------------------------------------------------------------------------- /cute/cvxqp2.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification QLR2-AN-V-V 13 | 14 | param N:=10000; 15 | param M:=N/4; 16 | 17 | var x{1..N} >= 0.1, <= 10.0, := 0.5; 18 | 19 | minimize f: 20 | sum {i in 1..N} (x[i]+x[((2*i-1) mod N)+1] 21 | +x[((3*i-1) mod N)+1])^2*i/2; 22 | subject to cons1{i in 1..M}: 23 | x[i]+2*x[((4*i-1) mod N)+1] + 3*x[((5*i-1) 24 | mod N)+1] - 6.0 = 0; 25 | -------------------------------------------------------------------------------- /cute/cvxqp3.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification QLR2-AN-V-V 13 | 14 | param N:=10000; 15 | param M:=3*N/4; 16 | 17 | var x{1..N} >= 0.1, <= 10.0, := 0.5; 18 | 19 | minimize f: 20 | sum {i in 1..N} (x[i]+x[((2*i-1) mod N)+1] 21 | +x[((3*i-1) mod N)+1])^2*i/2; 22 | subject to cons1{i in 1..M}: 23 | x[i]+2*x[((4*i-1) mod N)+1] + 3*x[((5*i-1) 24 | mod N)+1] - 6.0 = 0; 25 | -------------------------------------------------------------------------------- /cute/demymalo.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # V.F. Demynanov and V.N. Malozemov 14 | # "Introduction to Minimax" 15 | # Wiley, 1974 16 | 17 | # SIF input: Ph. Toint, Nov 1993. 18 | 19 | # classification LQR2-AN-3-3 20 | 21 | param xinit{1..2}; 22 | var x{i in 1..2} := xinit[i]; 23 | var u; 24 | minimize f: 25 | u; 26 | subject to cons1: 27 | -u+5*x[1]+x[2] <= 0; 28 | subject to cons2: 29 | -u-5*x[1]+x[2] <= 0; 30 | subject to cons3: 31 | -u+4*x[2]+x[1]^2+x[2]^2 <= 0; 32 | 33 | data; 34 | param xinit:= 1 1.0 2 1.0; 35 | -------------------------------------------------------------------------------- /cute/denschna.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: an example problem (p. 206) in 13 | # J.E. Dennis and R.B. Schnabel, 14 | # "Numerical Methods for Unconstrained Optimization and Nonlinear 15 | # Equations", 16 | # Prentice-Hall, Englewood Cliffs, 1983. 17 | 18 | # SIF input: Ph. Toint, Nov 1990. 19 | 20 | # classification OUR2-AN-2-0 21 | 22 | var x{1..2} := 1.0; 23 | minimize f: 24 | x[1]^4 + (x[1]+x[2])^2 + (-1.0+exp(x[2]))^2; 25 | -------------------------------------------------------------------------------- /cute/denschnb.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: an example problem (p. 201) in 13 | # J.E. Dennis and R.B. Schnabel, 14 | # "Numerical Methods for Unconstrained Optimization and Nonlinear 15 | # Equations", 16 | # Prentice-Hall, Englewood Cliffs, 1983. 17 | 18 | # SIF input: Ph. Toint, Nov 1990. 19 | 20 | # classification SUR2-AN-2-0 21 | 22 | var x{1..2} := 1.0; 23 | 24 | minimize f: 25 | (x[1]-2.0)^2 + ((x[1]-2.0)*x[2])^2 + (x[2]+1.0)^2; 26 | -------------------------------------------------------------------------------- /cute/denschnc.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: an example problem (p. 98) in 13 | # J.E. Dennis and R.B. Schnabel, 14 | # "Numerical Methods for Unconstrained Optimization and Nonlinear 15 | # Equations", 16 | # Prentice-Hall, Englewood Cliffs, 1983. 17 | 18 | # SIF input: Ph. Toint, Nov 1990. 19 | 20 | # classification SUR2-AN-2-0 21 | 22 | param xinit{1..2}; 23 | var x{i in 1..2} := xinit[i]; 24 | 25 | minimize f: 26 | (-2+x[1]^2+x[2]^2)^2 + (-2+exp(x[1]-1)+x[2]^3)^2; 27 | 28 | data; 29 | param xinit:= 1 2 2 3; 30 | -------------------------------------------------------------------------------- /cute/denschnd.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: an example problem (p. 83) in 13 | # J.E. Dennis and R.B. Schnabel, 14 | # "Numerical Methods for Unconstrained Optimization and Nonlinear 15 | # Equations", 16 | # Prentice-Hall, Englewood Cliffs, 1983. 17 | 18 | # SIF input: Ph. Toint, Nov 1990. 19 | 20 | # classification SUR2-AN-3-0 21 | 22 | var x{1..3} := 10.0; 23 | 24 | minimize f: 25 | (x[1]^2+x[2]^3-x[3]^4)^2 26 | +(2*x[1]*x[2]*x[3])^2 27 | +(2*x[1]*x[2]-3*x[2]*x[3]+x[1]*x[3])^2 28 | ; 29 | -------------------------------------------------------------------------------- /cute/denschne.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: an example problem (p. 107) in 13 | # J.E. Dennis and R.B. Schnabel, 14 | # "Numerical Methods for Unconstrained Optimization and Nonlinear 15 | # Equations", 16 | # Prentice-Hall, Englewood Cliffs, 1983. 17 | 18 | # SIF input: Ph. Toint, Nov 1990. 19 | 20 | # classification SUR2-AN-3-0 21 | 22 | param xinit{1..3}; 23 | var x{i in 1..3} := xinit[i]; 24 | 25 | minimize f: 26 | x[1]^2 + (x[2]+x[2]^2)^2 + (-1+exp(x[3]))^2; 27 | 28 | data; 29 | param xinit:= 30 | 1 2 31 | 2 3 32 | 3 -8; 33 | -------------------------------------------------------------------------------- /cute/denschnf.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: an example problem (p. 107) in 13 | # J.E. Dennis and R.B. Schnabel, 14 | # "Numerical Methods for Unconstrained Optimization and Nonlinear 15 | # Equations", 16 | # Prentice-Hall, Englewood Cliffs, 1983. 17 | 18 | # SIF input: Ph. Toint, Nov 1990. 19 | 20 | # classification SUR2-AY-2-0 21 | 22 | var x1 := 2; 23 | var x2 := 0; 24 | 25 | minimize f: 26 | (2*(x1+x2)^2+(x1-x2)^2-8)^2 27 | + (5*x1^2+(x2-3)^2-9)^2 28 | ; 29 | -------------------------------------------------------------------------------- /cute/dixon3dq.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: problem 156 (p. 51) in 13 | # A.R. Buckley, 14 | # "Test functions for unconstrained minimization", 15 | # TR 1989CS-3, Mathematics, statistics and computing centre, 16 | # Dalhousie University, Halifax (CDN), 1989. 17 | 18 | # SIF input: Ph. Toint, Dec 1989. 19 | 20 | # classification QUR2-AN-V-0 21 | 22 | param n := 10; 23 | 24 | var x {1..n} := -1.0; 25 | 26 | # rvdb comment: the sum should start at 1. 27 | minimize obj: (x[1]-1.0)^2 + sum {j in 2..n-1} (x[j]-x[j+1])^2 + (x[n]-1.0)^2; 28 | -------------------------------------------------------------------------------- /cute/dqdrtic.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: problem 22 in 13 | # Ph. L. Toint, 14 | # "Test problems for partially separable optimization and results 15 | # for the routine PSPMIN", 16 | # Report 83/4, Department of Mathematics, FUNDP (Namur, B), 1983. 17 | 18 | # SIF input: Ph. Toint, Dec 1989. 19 | 20 | # classification QUR2-AN-V-0 21 | 22 | param N:=5000; 23 | var x{1..N} := 3.0; 24 | 25 | minimize f: 26 | sum {i in 1..N-2} (100*x[i+1]^2+100*x[i+2]^2+x[i]^2); 27 | -------------------------------------------------------------------------------- /cute/dqrtic.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: problem 157 (p. 87) in 13 | # A.R. Buckley, 14 | # "Test functions for unconstrained minimization", 15 | # TR 1989CS-3, Mathematics, statistics and computing centre, 16 | # Dalhousie University, Halifax (CDN), 1989. 17 | 18 | # SIF input: Ph. Toint, Dec 1989. 19 | 20 | # classification OUR2-AN-V-0 21 | 22 | param N:=5000; 23 | var x{1..N} := 2.0; 24 | 25 | minimize f: 26 | sum {i in 1..N} (x[i]-i)^4; 27 | -------------------------------------------------------------------------------- /cute/dtoc2.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification OOR2-AN-V-V 13 | 14 | param n := 1000; 15 | param nx := 2; 16 | param ny := 4; 17 | param c{i in 1..ny, j in 1..nx} := (i+j)/(2*ny); 18 | 19 | var x{1..n-1,1..nx}; 20 | var y{1..n,1..ny}; 21 | 22 | minimize f: 23 | sum {t in 1..n-1} (sum {j in 1..ny} y[t,j]^2)*((sin(0.5*sum{j in 1..nx} x[t,j]^2))^2 + 1.0) + sum {j in 1..ny} y[n,j]^2; 24 | subject to cons1{t in 1..n-1,j in 1..ny}: 25 | sin(y[t,j]) + sum {i in 1..nx} c[j,i]*(sin(x[t,i])) -y[t+1,j] = 0; 26 | fix{i in 1..ny} y[1,i] := i/(2*ny); 27 | -------------------------------------------------------------------------------- /cute/dtoc3.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification QLR2-AN-V-V 13 | 14 | param n := 5000; 15 | param s := 1/n; 16 | 17 | var x{1..n-1}; 18 | var y{1..n,1..2}; 19 | 20 | minimize f: 21 | 0.5*s*(sum{t in 1..n-1} (2*y[t+1,1]^2 + y[t+1,2]^2 + 6*x[t]^2)); 22 | subject to cons1{t in 1..n-1}: 23 | y[t,1] - y[t+1,1] + s*y[t,2] = 0; 24 | subject to cons2{t in 1..n-1}: 25 | y[t,2] - y[t+1,2] - s*y[t,1] + s*x[t] = 0; 26 | 27 | fix y[1,1] := 15.0; 28 | fix y[1,2] := 5.0; 29 | -------------------------------------------------------------------------------- /cute/dtoc4.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification QOR2-AN-V-V 13 | 14 | param n := 5000; 15 | param h := 1/n; 16 | 17 | var x{1..n-1}; 18 | var y{1..n,1..2}; 19 | 20 | minimize f: 21 | 5*h*(0.5*y[1,1]^2+0.5*y[1,2]^2+x[1]^2 + sum {t in 2..n-1} (y[t,1]^2 + y[t,2]^2 + x[t]^2) + 0.5*y[n,1]^2 + 0.5*y[n,2]^2); 22 | subject to cons1{t in 1..n-1}: 23 | -y[t+1,1] + (1+5*h)*y[t,1] - 5*h*y[t,2] + 5*h*x[t] - 5*h*y[t,1]*y[t,2]^2= 0; 24 | subject to cons2{t in 1..n-1}: 25 | y[t,2] - y[t+1,2] + 5*h*y[t,1] = 0; 26 | fix y[1,1] := 0.0; 27 | fix y[1,2] := 1.0; 28 | -------------------------------------------------------------------------------- /cute/dtoc5.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification QQR2-AN-V-V 13 | 14 | param n := 5000; 15 | param h := 1/n; 16 | 17 | var x{1..n-1}; 18 | var y{1..n}; 19 | 20 | minimize f: 21 | sum {t in 1..n-1} (y[t]^2 + x[t]^2)/n; 22 | 23 | subject to cons1{t in 1..n-1}: 24 | h*y[t]^2 + y[t] - y[t+1] - h*x[t] = 0; 25 | fix y[1] := 1.0; 26 | -------------------------------------------------------------------------------- /cute/dtoc6.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification OOR2-AN-V-V 13 | 14 | param n := 5001; 15 | 16 | var x{1..n-1}; 17 | var y{1..n}; 18 | 19 | minimize f: 20 | sum {t in 1..n-1} ( 0.5*(exp(x[t])+y[t])^2 + 0.5*(x[t])^2 ); 21 | subject to cons1{t in 1..n-1}: 22 | y[t] - y[t+1] + exp(x[t]) = 0; 23 | fix y[1] := 0.0; 24 | -------------------------------------------------------------------------------- /cute/edensch.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # G. Li, 14 | # "The secant/finite difference algorithm for solving sparse 15 | # nonlinear systems of equations", 16 | # SIAM Journal on Optimization, (to appear), 1990. 17 | 18 | # SIF input: Ph. Toint, Apr 1990. 19 | # minor correction by Ph. Shott, January 1995. 20 | 21 | # classification OUR2-AN-V-0 22 | 23 | param N:=2000; 24 | var x{1..N} := 0.0; 25 | 26 | minimize f: 27 | sum {i in 1..N-1} ( (x[i]-2)^4 + (x[i]*x[i+1] 28 | -2*x[i+1])^2 + (x[i+1]+1)^2 ) + 16; 29 | -------------------------------------------------------------------------------- /cute/eg1.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # A.R. Conn, N. Gould and Ph.L. Toint, 14 | # "LANCELOT, A Fortran Package for Large-Scale Nonlinear Optimization 15 | # (Release A)" 16 | # Springer Verlag, 1992. 17 | 18 | # SIF input: N. Gould and Ph. Toint, June 1994. 19 | 20 | # classification OBR2-AY-3-0 21 | 22 | var x1; 23 | var x2 >= -1.0 , <= 1.0; 24 | var x3 >= 1.0 , <= 2.0; 25 | 26 | minimize obj: 27 | x1^2 + (x2*x3)^4 + x1*x3 + x2*sin(x1+x3) + x2; 28 | -------------------------------------------------------------------------------- /cute/eg2.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # A.R. Conn, N. Gould and Ph.L. Toint, 14 | # "LANCELOT, A Fortran Package for Large-Scale Nonlinear Optimization 15 | # (Release A)" 16 | # Springer Verlag, 1992. 17 | 18 | # SIF input: N. Gould and Ph. Toint, June 1994. 19 | 20 | # classification OUR2-AN-1000-0 21 | 22 | param N := 1000; 23 | 24 | var x{1..N}; 25 | 26 | minimize f: 27 | sum {i in 1..N-1} sin(x[1] + x[i]^2 - 1.0) + 0.5*sin(x[N]^2); 28 | -------------------------------------------------------------------------------- /cute/engval1.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: problem 31 in 13 | # Ph.L. Toint, 14 | # "Test problems for partially separable optimization and results 15 | # for the routine PSPMIN", 16 | # Report 83/4, Department of Mathematics, FUNDP (Namur, B), 1983. 17 | 18 | # See also Buckley#172 (p. 52) 19 | # SIF input: Ph. Toint and N. Gould, Dec 1989. 20 | 21 | # classification OUR2-AN-V-0 22 | 23 | param N:=5000; 24 | var x{1..N} := 2.0; 25 | 26 | minimize f: 27 | sum {i in 1..N-1} (x[i]^2+x[i+1]^2)^2 + sum {i in 1..N-1} (-4*x[i]+3.0); 28 | -------------------------------------------------------------------------------- /cute/expfit.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # A.R. Conn, N. Gould and Ph.L. Toint, 14 | # "LANCELOT, a Fortran package for large-scale nonlinear optimization", 15 | # Springer Verlag, FUNDP, 1992. 16 | 17 | # SIF input: Ph. Toint, Jan 1991. 18 | 19 | # classification SUR2-AN-2-0 20 | 21 | param p:=10; 22 | param h:=0.25; 23 | var alpha; 24 | var beta; 25 | minimize f: 26 | sum {i in 1..p} (alpha*exp(i*h*beta)-i*h)^2; 27 | -------------------------------------------------------------------------------- /cute/explin.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification OBR2-AN-V-V 13 | 14 | param n := 120; 15 | param m := 10; 16 | 17 | var x{1..n} >= 0, <= 10.0, := 0.0; 18 | 19 | minimize f: 20 | sum {i in 1..m} exp(0.1*x[i]*x[i+1]) + sum {i in 1..n} (-10.0*i*x[i]); 21 | -------------------------------------------------------------------------------- /cute/explin2.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification OBR2-AN-V-V 13 | 14 | param n := 120; 15 | param m := 10; 16 | 17 | var x{1..n} >= 0, <= 10.0, := 0.0; 18 | 19 | minimize f: 20 | sum {i in 1..m} exp(0.1*i*x[i]*x[i+1]/m) + sum {i in 1..n} (-10.0*i*x[i]); 21 | -------------------------------------------------------------------------------- /cute/expquad.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification OBR2-AN-V-V 13 | 14 | param n := 120; 15 | param m := 10; 16 | 17 | var x{1..n} := 0.0; 18 | 19 | minimize f: 20 | sum {i in 1..m} exp(0.1*i*m*x[i]*x[i+1]) + 21 | sum {i in m+1..n-1} (4.0*x[i]*x[i]+2.0*x[n]*x[n] + x[i]*x[n]) + 22 | sum {i in 1..n} (-10.0*i*x[i]); 23 | subject to cons{i in 1..m}: 24 | 0.0 <= x[i] <= 10.0; 25 | -------------------------------------------------------------------------------- /cute/extrasim.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # A.Conn, N. Gould, Ph. Toint 14 | # "LANCELOT, a Fortran package for large-scale nonlinear optimization" 15 | # Springer Verlag, 1992 16 | 17 | # SIF input: Ph. Toint, Dec 1991. 18 | 19 | # classification LLR2-AN-2-1 20 | 21 | var x >=0; 22 | var y; 23 | minimize f: 24 | x+1; 25 | subject to cons1: 26 | x+2*y-2.0 = 0; 27 | -------------------------------------------------------------------------------- /cute/extrosnb.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: problem 10 in 13 | # Ph.L. Toint, 14 | # "Test problems for partially separable optimization and results 15 | # for the routine PSPMIN", 16 | # Report 83/4, Department of Mathematics, FUNDP (Namur, B), 1983. 17 | 18 | # See also Buckley#116. Note that MGH#21 is the separable version. 19 | # SIF input: Ph. Toint, Dec 1989. 20 | 21 | # classification SUR2-AN-V-0 22 | 23 | param N:=10; 24 | var x{1..N} := 1; 25 | 26 | minimize f: 27 | (x[1]-1)^2 + sum {i in 2..N} 100*(x[i]-x[i-1]^2)^2; 28 | -------------------------------------------------------------------------------- /cute/fletchcr.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: The second problem given by 13 | # R. Fletcher, 14 | # "An optimal positive definite update for sparse Hessian matrices" 15 | # Numerical Analysis report NA/145, University of Dundee, 1992. 16 | 17 | # SIF input: Nick Gould, Oct 1992. 18 | 19 | # classification OUR2-AN-V-0 20 | 21 | param N:=100; 22 | var x{1..N} := 0.0; 23 | 24 | minimize f: 25 | sum {i in 1..N-1} 100*(x[i+1]-x[i]+1-x[i]^2)^2; 26 | -------------------------------------------------------------------------------- /cute/fletcher.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # R. Fletcher 14 | # "Practical Methods of Optimization", 15 | # second edition, Wiley, 1987. 16 | 17 | # SIF input: Ph. Toint, March 1994. 18 | 19 | # classification QOR2-AN-4-4 20 | 21 | var x{1..4} := 1; 22 | 23 | minimize f: 24 | x[1]*x[2]; 25 | subject to cons1: 26 | (x[1]*x[3]+x[2]*x[4])^2/(x[1]^2+x[2]^2) - x[3]^2 - x[4]^2 + 27 | 1= 0; 28 | subject to cons2: 29 | x[1]-x[3]-1 >= 0; 30 | subject to cons3: 31 | x[2]-x[4]-1 >= 0; 32 | subject to cons4: 33 | x[3]-x[4] >= 0; 34 | subject to cons5: 35 | x[4] >= 1; 36 | -------------------------------------------------------------------------------- /cute/genhumps.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # Ph. Toint, private communication, 1997. 14 | 15 | # SDIF input: N. Gould and Ph. Toint, November 1997. 16 | 17 | # classification SUR2-AN-V-0 18 | 19 | param zeta := 2; 20 | param N:=5; 21 | 22 | var x{i in 1..N} := if (i==1) then -506.0 else 506.2; 23 | 24 | minimize f: 25 | sum {i in 1..N-1} ( sin (zeta*x[i])^2*sin(zeta*x[i+1])^2+0.05*(x[i]^2+x[i+1]^2) ); 26 | -------------------------------------------------------------------------------- /cute/genrose.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: problem 5 in 13 | # S. Nash, 14 | # "Newton-type minimization via the Lanczos process", 15 | # SIAM J. Num. Anal. 21, 1984, 770-788. 16 | 17 | # SIF input: Nick Gould, Oct 1992. 18 | # minor correction by Ph. Shott, Jan 1995. 19 | 20 | # classification SUR2-AN-V-0 21 | 22 | param n := 500; 23 | 24 | var x{1..n} := 1/(n+1); 25 | 26 | minimize f: 27 | 1.0 + 28 | sum {i in 2..n} 100*(x[i]-x[i-1]^2)^2 + 29 | sum {i in 2..n} (x[i]-1.0)^2; 30 | -------------------------------------------------------------------------------- /cute/gigomez1.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # C. Gigola and S. Gomez, 14 | # "A Regularization Method for Solving the Finite Convex Min-Max Problem", 15 | # SINUM 27(6), pp. 1621-1634, 1990. 16 | 17 | # SIF input: Ph. Toint, August 1993. 18 | 19 | # classification LQR2-AN-3-3 20 | 21 | var x{1..2} := 2.0; 22 | var z:=2.0; 23 | minimize f: 24 | z; 25 | subject to cons1: 26 | z+5.0*x[1]-x[2] >= 0; 27 | subject to cons2: 28 | z-4*x[2]-x[1]^2-x[2]^2 >= 0; 29 | subject to cons3: 30 | z-5*x[1]-x[2] >= 0; 31 | -------------------------------------------------------------------------------- /cute/gilbert.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # J.Ch. Gilbert, 14 | # "On the Realization of the Wolfe Conditions in Reduced Quasi-Newton 15 | # Methods for Equality Constrained Optimization", 16 | # RR-2127, INRIA (F), 1993. 17 | 18 | # SIF input: Ph. Toint, April 1994 19 | 20 | # classification QQR2-AN-V-1 21 | 22 | param n := 1000; 23 | var x{i in 1..n} := (-1.0)^(i+1)*10.0; 24 | minimize f: 25 | sum {i in 1..n} ((n+1-i)*x[i]/n-1.0)^2/2; 26 | subject to cons1: 27 | (sum {i in 1..n} x[i]^2 - 1.0)/2 = 0.0; 28 | -------------------------------------------------------------------------------- /cute/goffin.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # M.M. Makela, 14 | # "Nonsmooth optimization", 15 | # Ph.D. thesis, Jyvaskyla University, 1990 16 | 17 | # SIF input: Ph. Toint, Nov 1993. 18 | 19 | # classification LLR2-AN-51-50 20 | 21 | param ri := 50; 22 | param t := -25.5 + (50); 23 | 24 | var x {j in 1..50} := -25.5+j; 25 | var u; 26 | 27 | minimize obj: u; 28 | 29 | subject to f {i in 1..50}: u >= 50*x[i] - sum {j in 1..50} x[j]; 30 | -------------------------------------------------------------------------------- /cute/gottfr.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: problem 208 (p. 56) in 13 | # A.R. Buckley, 14 | # "Test functions for unconstrained minimization", 15 | # TR 1989CS-3, Mathematics, statistics and computing centre, 16 | # Dalhousie University, Halifax (CDN), 1989. 17 | 18 | # SIF input: Ph. Toint, Dec 1989. 19 | 20 | # classification NQR2-AN-2-2 21 | 22 | var x{1..2} := 0.5; 23 | 24 | minimize f: 0; 25 | subject to cons: 26 | (x[1]-0.1136*(x[1]+3.0*x[2])*(1-x[1])) = 0; 27 | subject to cons2: 28 | (x[2]+7.5*(2.0*x[1]-x[2])*(1-x[2])) = 0; 29 | -------------------------------------------------------------------------------- /cute/gpp.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # Hans Mittelmann, private communication. 14 | 15 | # SIF input: N. Gould, Jan 1998 16 | 17 | # classification OOR2-AY-V-0 18 | 19 | param n:=250; 20 | var x{1..n} := 1.0; 21 | 22 | minimize f: 23 | sum {i in 1..n-1, j in i+1..n} exp(x[j]-x[i]); 24 | subject to cons1{i in 1..n-1}: 25 | x[i]+x[i+1] >= 0.0; 26 | subject to cons2{i in 1..n-1}: 27 | exp(x[i])+exp(x[i+1]) <= 20.0; 28 | -------------------------------------------------------------------------------- /cute/hager1.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: problem P1 in 13 | # W.W. Hager, 14 | # "Multiplier Methods for Nonlinear Optimal Control", 15 | # SIAM J. on Numerical Analysis 27(4): 1061-1080, 1990. 16 | 17 | # SIF input: Ph. Toint, March 1991. 18 | 19 | # classification SLR2-AN-V-V 20 | 21 | param N:=5000; 22 | var x{0..N} := 0.0; 23 | var u{1..N} := 0.0; 24 | 25 | minimize f: 26 | 0.5*x[N]^2 + sum {i in 1..N} (u[i]^2)/(2*N); 27 | subject to cons1{i in 1..N}: 28 | (N-0.5)*x[i] + (-N-0.5)*x[i-1] - u[i] = 0; 29 | subject to cons2: 30 | x[0] = 1.0; 31 | -------------------------------------------------------------------------------- /cute/hairy.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # Ph. Toint, private communication, 14 | 15 | # SIF input: Ph. Toint, Dec 1989. 16 | 17 | # classification OUR2-AY-2-0 18 | 19 | param hlength:=30; 20 | param cslope:=100; 21 | 22 | var x1 := -5; 23 | var x2 := -7; 24 | 25 | minimize f: 26 | sin(7*x1)^2*cos(7*x2)^2*hlength + 27 | cslope*sqrt(0.01+(x1-x2)^2) + cslope*sqrt(0.01+x1^2) 28 | ; 29 | -------------------------------------------------------------------------------- /cute/hatflda.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # "The OPTIMA user manual (issue No.8, p. 12)", 14 | # Numerical Optimization Centre, Hatfield Polytechnic (UK), 1989. 15 | 16 | # SIF input: Ph. Toint, May 1990. 17 | 18 | # classification SBR2-AN-4-0 19 | 20 | param N:=4; 21 | var x{1..N} := 0.1, >= 0.0000001; 22 | 23 | minimize f: 24 | (x[1]-1)^2 + sum {i in 2..N} (x[i-1]-sqrt(x[i]))^2; 25 | -------------------------------------------------------------------------------- /cute/hatfldb.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # "The OPTIMA user manual (issue No.8, p. 12)", 14 | # Numerical Optimization Centre, Hatfield Polytechnic (UK), 1989. 15 | 16 | # SIF input: Ph. Toint, May 1990. 17 | 18 | # classification SBR2-AN-4-0 19 | 20 | param N:=4; 21 | var x{1..N} := 0.1, >= 0.0000001; 22 | 23 | minimize f: 24 | (x[1]-1)^2 + sum {i in 2..N} (x[i-1]-sqrt(x[i]))^2; 25 | subject to cons1: 26 | x[2] <= 0.8; 27 | -------------------------------------------------------------------------------- /cute/hatfldc.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # "The OPTIMA user manual (issue No.8, p. 26)", 14 | # Numerical Optimization Centre, Hatfield Polytechnic (UK), 1989. 15 | 16 | # SIF input: Ph. Toint, May 1990. 17 | 18 | # classification SBR2-AN-25-0 19 | 20 | param N:=4; 21 | var x{1..N} := 0.9; 22 | 23 | minimize f: 24 | (x[1]-1)^2 + sum {i in 2..N-1} (x[i+1]-x[i]^2)^2 + (x[N]-1)^2; 25 | subject to cons1{i in 1..N-1}: 26 | 0.0 <= x[i] <= 10.0; 27 | -------------------------------------------------------------------------------- /cute/hatfldf.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # "The OPTIMA user manual (issue No.8, p. 47)", 14 | # Numerical Optimization Centre, Hatfield Polytechnic (UK), 1989. 15 | 16 | # SIF input: Ph. Toint, May 1990. 17 | 18 | # classification NOR2-AN-3-3 19 | 20 | var x{1..3} := 0.1; 21 | 22 | minimize f: 0; 23 | subject to cons1: 24 | (x[1]-0.032+x[2]*exp(x[3])) = 0; 25 | subject to cons2: 26 | (x[1]-0.056+x[2]*exp(2*x[3])) = 0; 27 | subject to cons3: 28 | (x[1]-0.099+x[2]*exp(3*x[3])) = 0; 29 | -------------------------------------------------------------------------------- /cute/hatfldg.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # "The OPTIMA user manual (issue No.8, p. 49)", 14 | # Numerical Optimization Centre, Hatfield Polytechnic (UK), 1989. 15 | 16 | # SIF input: Ph. Toint, May 1990. 17 | 18 | # classification NOR2-AY-25-25 19 | 20 | param N:=25; 21 | var x{1..N} := 1.0; 22 | 23 | minimize f: 0; 24 | subject to cons{i in 2..N-1}: 25 | ( x[i]*(x[i-1]-x[i+1])+x[i]-x[13]+1 ) = 0; 26 | subject to cons2: 27 | (x[1]-x[13]+1-x[1]*x[2]) = 0; 28 | subject to cons3: 29 | (x[N]-x[13]+1+x[N-1]*x[N]) = 0; 30 | -------------------------------------------------------------------------------- /cute/hilberta.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # K. Schittkowski, 14 | # "More Test Examples for Nonlinear Programming Codes", 15 | # Springer Verlag, Heidelberg, 1987. 16 | 17 | # See also Buckley#19 (p. 59) 18 | 19 | # SIF input: Ph. Toint, Dec 1989. 20 | 21 | # classification QUR2-AN-V-0 22 | 23 | param N := 10; 24 | 25 | var x{1..N}; 26 | param A{i in 1..N, j in 1..N} := 1/(i+j-1); 27 | 28 | minimize f: 29 | sum {i in 1..N} x[i]*(sum {j in 1..N}A[i,j]*x[j]); 30 | 31 | data; 32 | var x:= 33 | 1 -4 34 | 2 -2; 35 | -------------------------------------------------------------------------------- /cute/hilbertb.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: problem 19 (p. 59) in 13 | # A.R. Buckley, 14 | # "Test functions for unconstrained minimization", 15 | # TR 1989CS-3, Mathematics, statistics and computing centre, 16 | # Dalhousie University, Halifax (CDN), 1989. 17 | 18 | # SIF input: Ph. Toint, Dec 1989. 19 | 20 | # classification QUR2-AN-V-0 21 | 22 | param N:=50; 23 | param D:=5.0; 24 | var x{1..N} := -3.0; 25 | 26 | minimize f: 27 | sum {i in 1..N} (sum {j in 1..i-1} x[i]*x[j]/(i+j-1) + (x[i]^2)*(D+1/(4*i-2))); 28 | -------------------------------------------------------------------------------- /cute/himmelba.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: problem 25 in 13 | # D.H. Himmelblau, 14 | # "Applied nonlinear programming", 15 | # McGraw-Hill, New-York, 1972. 16 | 17 | # See Buckley#215 (p. 61) 18 | 19 | # SIF input: Ph. Toint, Dec 1989. 20 | 21 | # classification NLR2-AN-2-2 22 | 23 | param xinit{1..2}; 24 | var x{i in 1..2} := xinit[i]; 25 | minimize f: 0; 26 | subject to cons1: 27 | (4*x[1]-20) = 0; 28 | subject to cons2: 29 | (x[2]-6) = 0; 30 | 31 | data; 32 | param xinit:= 1 8.0 2 9.0; 33 | -------------------------------------------------------------------------------- /cute/himmelbb.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: problem 27 in 13 | # D.H. Himmelblau, 14 | # "Applied nonlinear programming", 15 | # McGraw-Hill, New-York, 1972. 16 | 17 | 18 | # See Buckley#77 (p. 62) 19 | 20 | # SIF input: Ph. Toint, Dec 1989. 21 | 22 | # classification OUR2-AN-2-0 23 | 24 | param xinit{1..2}; 25 | var x{i in 1..2} := xinit[i]; 26 | 27 | minimize f: 28 | (x[1]*x[2]*(1-x[1])*(1-x[2]-x[1]*(1-x[1]^5)))^2; 29 | 30 | data; 31 | param xinit:= 1 -1.2 2 1.0; 32 | -------------------------------------------------------------------------------- /cute/himmelbc.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: problem 28 in 13 | # D.H. Himmelblau, 14 | # "Applied nonlinear programming", 15 | # McGraw-Hill, New-York, 1972. 16 | 17 | # See Buckley#6 (p. 63) 18 | 19 | # SIF input: Ph. Toint, Dec 1989. 20 | 21 | # classification NQR2-AN-2-2 22 | 23 | var x{1..2}:=1.0; 24 | minimize f: 0; 25 | subject to cons1: 26 | (x[2]-11+x[1]^2) = 0; 27 | subject to cons2: 28 | (x[1]-7+x[2]^2) = 0; 29 | -------------------------------------------------------------------------------- /cute/himmelbd.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: problem 29 in 13 | # D.H. Himmelblau, 14 | # "Applied nonlinear programming", 15 | # McGraw-Hill, New-York, 1972. 16 | 17 | # See Buckley#86 (p. 64) 18 | 19 | # SIF input: Ph. Toint, Dec 1989. 20 | 21 | # classification NQR2-AN-2-2 22 | 23 | var x{1..2} := 1.0; 24 | minimize f: 0; 25 | subject to cons1: 26 | (12*x[2]-1.0+x[1]^2) = 0; 27 | subject to cons2: 28 | (84*x[1]+2324*x[2]-681.0+49*x[1]^2+49*x[2]^2) = 0; 29 | -------------------------------------------------------------------------------- /cute/himmelbe.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: problem 30 in 13 | # D.H. Himmelblau, 14 | # "Applied nonlinear programming", 15 | # McGraw-Hill, New-York, 1972. 16 | 17 | # See Buckley#88 (p. 65) 18 | 19 | # SIF input: Ph. Toint, Dec 1989. 20 | 21 | # classification NQR2-AY-3-3 22 | 23 | param xinit{1..3}; 24 | var x{i in 1..3}:= xinit[i]; 25 | minimize f: 0; 26 | subject to cons1: 27 | ( -x[3]+0.25*(x[1]+x[2])^2 ) = 0; 28 | subject to cons2: 29 | (-x[1]+1.0) = 0; 30 | subject to cons3: 31 | (-x[2]+1.0) = 0; 32 | 33 | data; 34 | param xinit:= 1 -1.2 2 2.0 3 2.0; 35 | -------------------------------------------------------------------------------- /cute/himmelbg.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: problem 33 in 13 | # D.H. Himmelblau, 14 | # "Applied nonlinear programming", 15 | # McGraw-Hill, New-York, 1972. 16 | 17 | # See Buckley#87 (p. 67) 18 | 19 | # SIF input: Ph. Toint, Dec 1989. 20 | 21 | # classification OUR2-AN-2-0 22 | 23 | var x{1..2} := 0.5; 24 | 25 | minimize f: 26 | exp(-x[1]-x[2])*(2*x[1]^2+3*x[2]^2); 27 | -------------------------------------------------------------------------------- /cute/himmelbh.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # D.H. Himmelblau, 14 | # "A uniform evaluation of unconstrained optimization techniques", 15 | # in "Numerical methods for nonlinear optimization" (F.A. Lootsma, ed.), 16 | # Academic Press, London, 1972. 17 | 18 | # See Buckley#8 (p. 60) 19 | 20 | # SIF input: Ph. Toint, Dec 1989. 21 | 22 | # classification OUR2-AN-2-0 23 | 24 | param xinit{1..2}; 25 | var x{i in 1..2} := xinit[i]; 26 | 27 | minimize f: 28 | -3*x[1]-2*x[2]+2+x[1]^3+x[2]^2; 29 | 30 | data; 31 | param xinit:= 1 0.0 2 2.0; 32 | -------------------------------------------------------------------------------- /cute/hong.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: Se June Hong/Chid Apte 13 | 14 | # SIF input: A.R.Conn, Jan 1991. 15 | 16 | # classification OLR2-AN-4-1 17 | 18 | var T{1..4} >= 0.0, <= 1.0, := 0.5; 19 | 20 | minimize f: 21 | 0.92+0.08*exp(0.38*25*T[1]) - 2.95+3.95*exp(0.11*50*T[2]) - 1.66+1657834*exp(-1.48*(9.0+4.0*T[3])) + 0.11+0.89*exp(0.00035*20000*T[4]); 22 | 23 | subject to cons1: 24 | T[1]+T[2]+T[3]+T[4]-1.0 = 0; 25 | -------------------------------------------------------------------------------- /cute/hs001.mod: -------------------------------------------------------------------------------- 1 | var x {1..2}; 2 | 3 | minimize obj: 4 | 100*(x[2] - x[1]^2)^2 + (1-x[1])^2; 5 | ; 6 | 7 | subject to constr: -1.5 <= x[2]; 8 | 9 | let x[1] := -2; 10 | let x[2] := 1; 11 | -------------------------------------------------------------------------------- /cute/hs002.mod: -------------------------------------------------------------------------------- 1 | var x {j in 1..2}; 2 | 3 | minimize obj: 4 | 100*(x[2] - x[1]^2)^2 + (1-x[1])^2; 5 | ; 6 | 7 | subject to constr: 1.5 <= x[2]; 8 | 9 | let x[1] := -2; 10 | let x[2] := 1; 11 | -------------------------------------------------------------------------------- /cute/hs003.mod: -------------------------------------------------------------------------------- 1 | var x {1..2}; 2 | 3 | minimize obj: 4 | x[2] + 0.00001*(x[2]-x[1])^2 5 | ; 6 | 7 | subject to constr: 0 <= x[2]; 8 | 9 | let x[1] := 10; 10 | let x[2] := 1; 11 | -------------------------------------------------------------------------------- /cute/hs004.mod: -------------------------------------------------------------------------------- 1 | var x {1..2}; 2 | 3 | minimize obj: 4 | (x[1]+1)^3/3 + x[2] 5 | ; 6 | 7 | subject to constr1: 1 <= x[1]; 8 | subject to constr2: 0 <= x[2]; 9 | 10 | let x[1] := 1.125; 11 | let x[2] := 0.125; 12 | -------------------------------------------------------------------------------- /cute/hs005.mod: -------------------------------------------------------------------------------- 1 | var x {1..2}; 2 | 3 | minimize obj: 4 | sin(x[1]+x[2]) + (x[1]-x[2])^2 - 1.5*x[1] + 2.5*x[2] + 1 5 | ; 6 | 7 | subject to constr1: -1.5 <= x[1] <= 4; 8 | subject to constr2: -3 <= x[2] <= 3; 9 | 10 | let x[1] := 0; 11 | let x[2] := 0; 12 | -------------------------------------------------------------------------------- /cute/hs006.mod: -------------------------------------------------------------------------------- 1 | var x {1..2}; 2 | 3 | minimize obj: 4 | (1-x[1])^2 5 | ; 6 | 7 | subject to constr: 10*(x[2] - x[1]^2) = 0; 8 | 9 | let x[1] := -1.2; 10 | let x[2] := 1; 11 | 12 | #printf "optimal x as starting point \n"; 13 | #let x[1] := 1; 14 | #let x[2] := 1; 15 | -------------------------------------------------------------------------------- /cute/hs007.mod: -------------------------------------------------------------------------------- 1 | var x {1..2}; 2 | 3 | minimize obj: 4 | log(1+x[1]^2) - x[2] 5 | ; 6 | 7 | subject to constr: (1+x[1]^2)^2 + x[2]^2 = 4; 8 | 9 | let x[1] := 2; 10 | let x[2] := 2; 11 | 12 | #printf "optimal solution as starting point \n"; 13 | #let x[1] := 0; 14 | #let x[2] := 1.73205; 15 | -------------------------------------------------------------------------------- /cute/hs008.mod: -------------------------------------------------------------------------------- 1 | var x {1..2}; 2 | 3 | minimize obj: 4 | -1 5 | ; 6 | 7 | subject to constr1: x[1]^2 + x[2]^2 = 25; 8 | subject to constr2: x[1]*x[2] = 9; 9 | 10 | let x[1] := 2; 11 | let x[2] := 1; 12 | 13 | #printf "optimal solution as starting point \n"; 14 | #let x[1] := 4.60159; 15 | #let x[2] := 1.95584; 16 | -------------------------------------------------------------------------------- /cute/hs009.mod: -------------------------------------------------------------------------------- 1 | param pi := 3.14159; 2 | 3 | var x {1..2}; 4 | 5 | minimize obj: 6 | sin(pi * x[1] / 12) * cos(pi * x[2] / 16); 7 | ; 8 | 9 | subject to constr1: 4*x[1] - 3*x[2] = 0; 10 | 11 | let x[1] := 0; 12 | let x[2] := 0; 13 | 14 | #printf "optimal solution as starting point \n"; 15 | #let x[1] := -3; 16 | #let x[2] := -4; 17 | -------------------------------------------------------------------------------- /cute/hs010.mod: -------------------------------------------------------------------------------- 1 | var x {1..2}; 2 | 3 | minimize obj: 4 | x[1] - x[2] 5 | ; 6 | 7 | subject to constr1: -3*x[1]^2 + 2*x[1]*x[2] - x[2]^2 >= -1; 8 | 9 | let x[1] := -10; 10 | let x[2] := 10; 11 | 12 | #printf "optimal solution as starting point \n"; 13 | #let x[1] := 0; 14 | #let x[2] := 1; 15 | 16 | # 17 | -------------------------------------------------------------------------------- /cute/hs011.mod: -------------------------------------------------------------------------------- 1 | var x {1..2}; 2 | 3 | minimize obj: 4 | (x[1] - 5)^2 + x[2]^2 -25 5 | ; 6 | 7 | subject to constr1: x[1]^2 <= x[2]; 8 | 9 | let x[1] := 4.9; 10 | let x[2] := 0.1; 11 | 12 | #printf "optimal solution as starting point \n"; 13 | #let x[1] := 1.23477; 14 | #let x[2] := 1.52466; 15 | -------------------------------------------------------------------------------- /cute/hs012.mod: -------------------------------------------------------------------------------- 1 | var x {1..2}; 2 | 3 | minimize obj: 4 | x[1]^2/2 + x[2]^2 - x[1]*x[2] - 7*x[1] - 7*x[2] 5 | ; 6 | 7 | subject to constr1: 4*x[1]^2 + x[2]^2 <= 25; 8 | 9 | let x[1] := 0; 10 | let x[2] := 0; 11 | 12 | #printf "optimal solution as starting point \n"; 13 | #let x[1] := 2; 14 | #let x[2] := 3; 15 | -------------------------------------------------------------------------------- /cute/hs013.mod: -------------------------------------------------------------------------------- 1 | var x {1..2} >= 0; 2 | 3 | minimize obj: 4 | (x[1] - 2)^2 + x[2]^2 5 | ; 6 | 7 | subject to constr1: (1-x[1])^3 >= x[2]; 8 | 9 | let x[1] := -2; 10 | let x[2] := -2; 11 | 12 | #printf "optimal solution as starting point \n"; 13 | #let x[1] := 1; 14 | #let x[2] := 0; 15 | -------------------------------------------------------------------------------- /cute/hs014.mod: -------------------------------------------------------------------------------- 1 | var x {1..2}; 2 | 3 | minimize obj: 4 | (x[1] - 2)^2 + (x[2]-1)^2 5 | ; 6 | 7 | subject to constr1: x[1]^2/4 + x[2]^2 <= 1; 8 | subject to constr2: x[1] - 2*x[2] = -1; 9 | 10 | let x[1] := 2; 11 | let x[2] := 2; 12 | 13 | #printf "optimal solution as starting point \n"; 14 | #let x[1] := 0.822876; 15 | #let x[2] := 0.911438; 16 | -------------------------------------------------------------------------------- /cute/hs015.mod: -------------------------------------------------------------------------------- 1 | var x {1..2}; 2 | 3 | minimize obj: 4 | 100*(x[2] - x[1]^2)^2 + (1 - x[1])^2 5 | ; 6 | 7 | subject to constr1: x[1]*x[2] >= 1; 8 | subject to constr2: x[1] + x[2]^2 >= 0; 9 | subject to constr3: x[1] <= 1/2; 10 | 11 | let x[1] := -2; 12 | let x[2] := 1; 13 | 14 | #printf "optimal solution as starting point \n"; 15 | #let x[1] := 0.5; 16 | #let x[2] := 2; 17 | -------------------------------------------------------------------------------- /cute/hs016.mod: -------------------------------------------------------------------------------- 1 | var x {1..2}; 2 | 3 | minimize obj: 4 | 100*(x[2] - x[1]^2)^2 + (1 - x[1])^2 5 | ; 6 | 7 | subject to constr1: x[1]^2 + x[2] >= 0; 8 | subject to constr2: x[1] + x[2]^2 >= 0; 9 | subject to constr3: -1/2 <= x[1] <= 1/2; 10 | subject to constr4: x[2] <= 1; 11 | 12 | let x[1] := -2; 13 | let x[2] := 1; 14 | 15 | #printf "optimal solution as starting point \n"; 16 | #let x[1] := 0.5; 17 | #let x[2] := 0.25; 18 | -------------------------------------------------------------------------------- /cute/hs017.mod: -------------------------------------------------------------------------------- 1 | var x {1..2}; 2 | 3 | minimize obj: 4 | 100*(x[2] - x[1]^2)^2 + (1 - x[1])^2 5 | ; 6 | 7 | subject to constr1: -x[1] + x[2]^2 >= 0; 8 | subject to constr2: x[1]^2 - x[2] >= 0; 9 | subject to constr3: -1/2 <= x[1] <= 1/2; 10 | subject to constr4: x[2] <= 1; 11 | 12 | let x[1] := -2; 13 | let x[2] := 1; 14 | 15 | #printf "optimal solution as starting point \n"; 16 | #let x[1] := 0; 17 | #let x[2] := 0; 18 | -------------------------------------------------------------------------------- /cute/hs018.mod: -------------------------------------------------------------------------------- 1 | var x {1..2}; 2 | 3 | minimize obj: 4 | x[1]^2/100 + x[2]^2 5 | ; 6 | 7 | subject to constr1: x[1]*x[2] >= 25; 8 | subject to constr2: x[1]^2 + x[2]^2 >= 25; 9 | subject to constr3: 2 <= x[1] <= 50; 10 | subject to constr4: 0 <= x[2] <= 50; 11 | 12 | let x[1] := 2; 13 | let x[2] := 2; 14 | 15 | #printf "optimal solution as starting point \n"; 16 | #let x[1] := 15.8114; 17 | #let x[2] := 1.58114; 18 | -------------------------------------------------------------------------------- /cute/hs019.mod: -------------------------------------------------------------------------------- 1 | var x {1..2}; 2 | 3 | minimize obj: 4 | (x[1] - 10)^3 + (x[2] - 20)^3 5 | # (x[1] - 10)* (x[1] - 10)* (x[1] - 10) 6 | # + 7 | # (x[2] - 20)* (x[2] - 20)* (x[2] - 20) 8 | ; 9 | 10 | subject to constr1: (x[1] - 5)^2 + (x[2] - 5)^2 >= 100; 11 | subject to constr2: (x[2] - 5)^2 + (x[1] - 6)^2 <= 82.81; 12 | subject to constr3: 13 <= x[1] <= 100; 13 | subject to constr4: 0 <= x[2] <= 100; 14 | 15 | let x[1] := 20.1; 16 | let x[2] := 5.84; 17 | 18 | #printf "optimal solution as starting point \n"; 19 | #let x[1] := 14.095; 20 | #let x[2] := 0.84296079; 21 | -------------------------------------------------------------------------------- /cute/hs020.mod: -------------------------------------------------------------------------------- 1 | var x {1..2}; 2 | 3 | minimize obj: 4 | 100*(x[2] - x[1]^2)^2 + (1-x[1])^2 5 | ; 6 | 7 | subject to constr1: x[1] + x[2]^2 >= 0; 8 | subject to constr2: x[1]^2 + x[2] >= 0; 9 | subject to constr3: x[1]^2 + x[2]^2 >= 1; 10 | subject to constr4: -1/2 <= x[1] <= 1/2; 11 | 12 | let x[1] := -2; 13 | let x[2] := 1; 14 | 15 | #printf "optimal solution as starting point \n"; 16 | #let x[1] := 1/2; 17 | #let x[2] := 1/(2*sqrt(3)); 18 | -------------------------------------------------------------------------------- /cute/hs021.mod: -------------------------------------------------------------------------------- 1 | var x {1..2}; 2 | 3 | minimize obj: 4 | x[1]^2/100 + x[2]^2 - 100 5 | ; 6 | 7 | subject to constr1: 10*x[1] - x[2] >= 10; 8 | subject to constr2: 2 <= x[1] <= 50; 9 | subject to constr3: -50 <= x[2] <= 50; 10 | 11 | let x[1] := -1; 12 | let x[2] := -1; 13 | 14 | #printf "optimal solution as starting point \n"; 15 | #let x[1] := 2.00265; 16 | #let x[2] := 0; 17 | -------------------------------------------------------------------------------- /cute/hs022.mod: -------------------------------------------------------------------------------- 1 | var x {1..2}; 2 | 3 | minimize obj: 4 | (x[1] - 2)^2 + (x[2] - 1)^2 5 | ; 6 | 7 | subject to constr1: x[1] + x[2] <= 2; 8 | subject to constr2: -x[1]^2 + x[2] >= 0; 9 | 10 | let x[1] := 2; 11 | let x[2] := 2; 12 | 13 | #printf "optimal solution as starting point \n"; 14 | #let x[1] := 1; 15 | #let x[2] := 1; 16 | -------------------------------------------------------------------------------- /cute/hs023.mod: -------------------------------------------------------------------------------- 1 | var x {1..2} <= 50, >= -50; 2 | 3 | minimize obj: 4 | x[1]^2 + x[2]^2 5 | ; 6 | 7 | subject to constr1: x[1] + x[2] >= 1; 8 | subject to constr2: x[1]^2 + x[2]^2 >= 1; 9 | subject to constr3: 9*x[1]^2 + x[2]^2 >= 9; 10 | subject to constr4: x[1]^2 - x[2] >= 0; 11 | subject to constr5: x[2]^2 - x[1] >= 0; 12 | 13 | let x[1] := 3; 14 | let x[2] := 1; 15 | 16 | #printf "optimal solution as starting point \n"; 17 | #let x[1] := 1; 18 | #let x[2] := 1; 19 | -------------------------------------------------------------------------------- /cute/hs024.mod: -------------------------------------------------------------------------------- 1 | var x {1..2} >= 0; 2 | 3 | minimize obj: 4 | ((x[1] - 3)^2 - 9) * x[2]^3 / (27*sqrt(3)) 5 | ; 6 | 7 | subject to constr1: x[1]/sqrt(3) - x[2] >= 0; 8 | subject to constr2: x[1] + sqrt(3)*x[2] >= 0; 9 | subject to constr3: -x[1] - sqrt(3)*x[2] >= -6; 10 | 11 | let x[1] := 1; 12 | let x[2] := 1/2; 13 | 14 | #printf "optimal solution as starting point \n"; 15 | #let x[1] := 3; 16 | #let x[2] := 1.73205; 17 | -------------------------------------------------------------------------------- /cute/hs025.mod: -------------------------------------------------------------------------------- 1 | var x {1..3}; 2 | 3 | param u {i in 1..99} := 25 + (-50*log(i/100))^(2/3); 4 | 5 | minimize obj: 6 | sum {i in 1..99} 7 | ( 8 | -i/100 + exp(-(u[i] - x[2])^x[3]/x[1]) 9 | )^2 10 | ; 11 | 12 | subject to constr1: 1/10 <= x[1] <= 100; 13 | subject to constr2: 0 <= x[2] <= 25.6; 14 | subject to constr3: 0 <= x[3] <= 5; 15 | 16 | let x[1] := 100; 17 | let x[2] := 12.5; 18 | let x[3] := 3; 19 | 20 | #printf "optimal solution as starting point \n"; 21 | #let x[1] := ? 22 | #let x[2] := ? 23 | #let x[3] := ? 24 | -------------------------------------------------------------------------------- /cute/hs026.mod: -------------------------------------------------------------------------------- 1 | var x {1..3}; 2 | 3 | minimize obj: 4 | (x[1] - x[2])^2 + (x[2] - x[3])^4 5 | ; 6 | 7 | subject to constr1: (1 + x[2]^2)*x[1] + x[3]^4 = 3; 8 | 9 | let x[1] := -2.6; 10 | let x[2] := 2; 11 | let x[3] := 2; 12 | 13 | #printf "optimal solution as starting point \n"; 14 | #let x[1] := 1; 15 | #let x[2] := 1; 16 | #let x[3] := 1; 17 | -------------------------------------------------------------------------------- /cute/hs027.mod: -------------------------------------------------------------------------------- 1 | var x {1..3}; 2 | 3 | minimize obj: 4 | (x[1] - 1)^2/100 + (x[2] - x[1]^2)^2 5 | ; 6 | 7 | subject to constr1: x[1] + x[3]^2 = -1; 8 | 9 | let x[1] := 2; 10 | let x[2] := 2; 11 | let x[3] := 2; 12 | 13 | #printf "optimal solution as starting point \n"; 14 | #let x[1] := -1; 15 | #let x[2] := 1; 16 | #let x[3] := 0; 17 | -------------------------------------------------------------------------------- /cute/hs028.mod: -------------------------------------------------------------------------------- 1 | var x {1..3}; 2 | 3 | minimize obj: 4 | (x[1] + x[2])^2 + (x[2] + x[3])^2 5 | ; 6 | 7 | subject to constr1: x[1] + 2*x[2] + 3*x[3] = 1; 8 | 9 | let x[1] := -4; 10 | let x[2] := 1; 11 | let x[3] := 1; 12 | 13 | #printf "optimal solution as starting point \n"; 14 | #let x[1] := 0.5; 15 | #let x[2] := -0.5; 16 | #let x[3] := 0.5; 17 | -------------------------------------------------------------------------------- /cute/hs029.mod: -------------------------------------------------------------------------------- 1 | var x {1..3}; 2 | 3 | minimize obj: 4 | -x[1]*x[2]*x[3] 5 | ; 6 | 7 | subject to constr1: x[1]^2 + 2*x[2]^2 + 4*x[3]^2 <= 48; 8 | 9 | let x[1] := 1; 10 | let x[2] := 1; 11 | let x[3] := 1; 12 | 13 | #printf "optimal solution as starting point \n"; 14 | #let x[1] := 4; 15 | #let x[2] := 2.82843; 16 | #let x[3] := 2; 17 | -------------------------------------------------------------------------------- /cute/hs030.mod: -------------------------------------------------------------------------------- 1 | var x {1..3}; 2 | 3 | minimize obj: 4 | x[1]^2 + x[2]^2 + x[3]^2 5 | ; 6 | 7 | subject to constr1: x[1]^2 + x[2]^2 <= 1; 8 | subject to constr2: 1 <= x[1] <= 10; 9 | subject to constr3: -10 <= x[2] <= 10; 10 | subject to constr4: -10 <= x[3] <= 10; 11 | 12 | let x[1] := 1; 13 | let x[2] := 1; 14 | let x[3] := 1; 15 | 16 | #printf "optimal solution as starting point \n"; 17 | #let x[1] := 1; 18 | #let x[2] := 0; 19 | #let x[3] := 0; 20 | -------------------------------------------------------------------------------- /cute/hs031.mod: -------------------------------------------------------------------------------- 1 | var x {1..3}; 2 | 3 | minimize obj: 4 | 9*x[1]^2 + x[2]^2 + 9*x[3]^2 5 | ; 6 | 7 | subject to constr1: x[1] * x[2] >= 1; 8 | subject to constr2: -10 <= x[1] <= 10; 9 | subject to constr3: 1 <= x[2] <= 10; 10 | subject to constr4: -10 <= x[3] <= 1; 11 | 12 | let x[1] := 1; 13 | let x[2] := 1; 14 | let x[3] := 1; 15 | 16 | #printf "optimal solution as starting point \n"; 17 | #let x[1] := 0.57735; 18 | #let x[2] := 1.73205; 19 | #let x[3] := 0; 20 | -------------------------------------------------------------------------------- /cute/hs032.mod: -------------------------------------------------------------------------------- 1 | var x {1..3} >= 0; 2 | 3 | minimize obj: 4 | (x[1] + 3*x[2] + x[3])^2 + 4*(x[1] - x[2])^2 5 | ; 6 | 7 | subject to constr1: 6*x[2] + 4*x[3] - x[1]^3 >= 3; 8 | subject to constr2: x[1] + x[2] + x[3] = 1; 9 | 10 | let x[1] := 0.1; 11 | let x[2] := 0.7; 12 | let x[3] := 0.2; 13 | 14 | #printf "optimal solution as starting point \n"; 15 | #let x[1] := 0; 16 | #let x[2] := 0; 17 | #let x[3] := 1; 18 | -------------------------------------------------------------------------------- /cute/hs033.mod: -------------------------------------------------------------------------------- 1 | var x {1..3} >= 0; 2 | 3 | minimize obj: 4 | (x[1] - 1)*(x[1] - 2)*(x[1] - 3) + x[3] 5 | ; 6 | 7 | subject to constr1: x[1]^2 + x[2]^2 <= x[3]^2; 8 | subject to constr2: x[1]^2 + x[2]^2 + x[3]^2 >= 4; 9 | subject to constr3: x[3] <= 5; 10 | 11 | let x[1] := 0; 12 | let x[2] := 0; 13 | let x[3] := 3; 14 | 15 | #printf "optimal solution as starting point \n"; 16 | #let x[1] := 0; 17 | #let x[2] := sqrt(2); 18 | #let x[3] := sqrt(2); 19 | -------------------------------------------------------------------------------- /cute/hs034.mod: -------------------------------------------------------------------------------- 1 | var x {1..3} >= 0; 2 | 3 | minimize obj: 4 | -x[1] 5 | ; 6 | 7 | subject to constr1: x[2] >= exp(x[1]); 8 | subject to constr2: x[3] >= exp(x[2]); 9 | subject to constr3: x[1] <= 100; 10 | subject to constr4: x[2] <= 100; 11 | subject to constr5: x[3] <= 10; 12 | 13 | let x[1] := 0; 14 | let x[2] := 1.05; 15 | let x[3] := 2.9; 16 | 17 | #printf "optimal solution as starting point \n"; 18 | #let x[1] := 0.83403; 19 | #let x[2] := 2.30258; 20 | #let x[3] := 10; 21 | -------------------------------------------------------------------------------- /cute/hs035.mod: -------------------------------------------------------------------------------- 1 | var x {1..3} >= 0; 2 | 3 | minimize obj: 4 | 9 - 8*x[1] - 6*x[2] - 4*x[3] + 2*x[1]^2 + 2*x[2]^2 + x[3]^2 5 | + 2*x[1]*x[2] + 2*x[1]*x[3] 6 | ; 7 | 8 | subject to constr1: x[1] + x[2] + 2*x[3] <= 3; 9 | 10 | let x[1] := 0.5; 11 | let x[2] := 0.5; 12 | let x[3] := 0.5; 13 | 14 | #printf "optimal solution as starting point \n"; 15 | #let x[1] := 4/3; 16 | #let x[2] := 7/9; 17 | #let x[3] := 4/9; 18 | -------------------------------------------------------------------------------- /cute/hs036.mod: -------------------------------------------------------------------------------- 1 | var x {1..3} >= 0; 2 | 3 | minimize obj: 4 | -x[1]*x[2]*x[3] 5 | ; 6 | 7 | subject to constr1: x[1] + 2*x[2] + 2*x[3] <= 72; 8 | subject to constr2: x[1] <= 20; 9 | subject to constr3: x[2] <= 11; 10 | subject to constr4: x[3] <= 42; 11 | 12 | let x[1] := 10; 13 | let x[2] := 10; 14 | let x[3] := 10; 15 | 16 | #printf "optimal solution as starting point \n"; 17 | #let x[1] := 20; 18 | #let x[2] := 11; 19 | #let x[3] := 15; 20 | -------------------------------------------------------------------------------- /cute/hs037.mod: -------------------------------------------------------------------------------- 1 | var x {1..3} >= 0, <= 42; 2 | 3 | minimize obj: 4 | -x[1]*x[2]*x[3] 5 | ; 6 | 7 | subject to constr1: x[1] + 2*x[2] + 2*x[3] <= 72; 8 | subject to constr2: x[1] + 2*x[2] + 2*x[3] >= 0; 9 | 10 | let x[1] := 10; 11 | let x[2] := 10; 12 | let x[3] := 10; 13 | 14 | #printf "optimal solution as starting point \n"; 15 | #let x[1] := 24; 16 | #let x[2] := 12; 17 | #let x[3] := 12; 18 | -------------------------------------------------------------------------------- /cute/hs038.mod: -------------------------------------------------------------------------------- 1 | var x {1..4} >= -10, <= 10; 2 | 3 | minimize obj: 4 | 100*(x[2]-x[1]^2)^2 + (1-x[1])^2 + 90*(x[4]-x[3]^2)^2 + (1-x[3])^2 5 | + 10.1*( (x[2]-1)^2 + (x[4]-1)^2 ) + 19.8*(x[2]-1)*(x[4]-1) 6 | ; 7 | 8 | #subject to constr1: x[1] + 2*x[2] + 2*x[3] <= 72; 9 | #subject to constr2: x[1] + 2*x[2] + 2*x[3] >= 0; 10 | 11 | let x[1] := -3; 12 | let x[2] := -1; 13 | let x[3] := -3; 14 | let x[4] := -1; 15 | 16 | #printf "optimal solution as starting point \n"; 17 | #let x[1] := 1; 18 | #let x[2] := 1; 19 | #let x[3] := 1; 20 | #let x[4] := 1; 21 | -------------------------------------------------------------------------------- /cute/hs039.mod: -------------------------------------------------------------------------------- 1 | var x {1..4}; 2 | 3 | minimize obj: 4 | -x[1] 5 | ; 6 | 7 | subject to constr1: x[2] - x[1]^3 - x[3]^2 = 0; 8 | subject to constr2: x[1]^2 - x[2] - x[4]^2 = 0; 9 | 10 | let x[1] := 2; 11 | let x[2] := 2; 12 | let x[3] := 2; 13 | let x[4] := 2; 14 | 15 | #printf "optimal solution as starting point \n"; 16 | #let x[1] := 1; 17 | #let x[2] := 1; 18 | #let x[3] := 0; 19 | #let x[4] := 0; 20 | -------------------------------------------------------------------------------- /cute/hs040.mod: -------------------------------------------------------------------------------- 1 | var x {1..4}; 2 | 3 | minimize obj: 4 | -x[1]*x[2]*x[3]*x[4] 5 | ; 6 | 7 | subject to constr1: x[1]^3 + x[2]^2 = 1; 8 | subject to constr2: x[1]^2*x[4] - x[3] = 0; 9 | subject to constr3: x[4]^2 - x[2] = 0; 10 | 11 | let x[1] := 0.8; 12 | let x[2] := 0.8; 13 | let x[3] := 0.8; 14 | let x[4] := 0.8; 15 | 16 | #printf "optimal solution as starting point \n"; 17 | #let x[1] := 0.793701; 18 | #let x[2] := 0.707107; 19 | #let x[3] := 0.529732; 20 | #let x[4] := 0.840896; 21 | -------------------------------------------------------------------------------- /cute/hs041.mod: -------------------------------------------------------------------------------- 1 | var x {1..4} >= 0; 2 | 3 | minimize obj: 4 | 2-x[1]*x[2]*x[3] 5 | ; 6 | 7 | subject to constr1: x[1] + 2*x[2] + 2*x[3] - x[4] = 0; 8 | subject to constr2: x[1] <= 1; 9 | subject to constr3: x[2] <= 1; 10 | subject to constr4: x[3] <= 1; 11 | subject to constr5: x[4] <= 2; 12 | 13 | let x[1] := 2; 14 | let x[2] := 2; 15 | let x[3] := 2; 16 | let x[4] := 2; 17 | 18 | #printf "optimal solution as starting point \n"; 19 | #let x[1] := 2/3; 20 | #let x[2] := 1/3; 21 | #let x[3] := 1/3; 22 | #let x[4] := 2; 23 | -------------------------------------------------------------------------------- /cute/hs042.mod: -------------------------------------------------------------------------------- 1 | var x {1..4} >= 0; 2 | 3 | minimize obj: 4 | (x[1]-1)^2 + (x[2]-2)^2 + (x[3]-3)^2 + (x[4]-4)^2 5 | ; 6 | 7 | subject to constr1: x[1] = 2; 8 | subject to constr2: x[3]^2 + x[4]^2 = 2; 9 | 10 | let x[1] := 1; 11 | let x[2] := 1; 12 | let x[3] := 1; 13 | let x[4] := 1; 14 | 15 | #printf "optimal solution as starting point \n"; 16 | #let x[1] := 2; 17 | #let x[2] := 2; 18 | #let x[3] := 0.848529; 19 | #let x[4] := 1.13137; 20 | -------------------------------------------------------------------------------- /cute/hs043.mod: -------------------------------------------------------------------------------- 1 | var x {1..4}; 2 | 3 | minimize obj: 4 | x[1]^2 + x[2]^2 + 2*x[3]^2 + x[4]^2 - 5*x[1] - 5*x[2] - 21*x[3] + 7*x[4] 5 | ; 6 | 7 | subject to constr1: x[1]^2 +x[2]^2 +x[3]^2 +x[4]^2 +x[1] -x[2] +x[3] -x[4] <= 8; 8 | subject to constr2: x[1]^2 +2*x[2]^2 +x[3]^2 +2*x[4]^2 -x[1] -x[4] <= 10; 9 | subject to constr3: 2*x[1]^2 +x[2]^2 +x[3]^2 +2*x[1] -x[2] -x[4] <= 5; 10 | 11 | let x[1] := 0; 12 | let x[2] := 0; 13 | let x[3] := 0; 14 | let x[4] := 0; 15 | 16 | #printf "optimal solution as starting point \n"; 17 | #let x[1] := 0; 18 | #let x[2] := 1; 19 | #let x[3] := 2; 20 | #let x[4] := -1; 21 | -------------------------------------------------------------------------------- /cute/hs044.mod: -------------------------------------------------------------------------------- 1 | var x {1..4} >= 0; 2 | 3 | minimize obj: 4 | x[1] - x[2] - x[3] - x[1]*x[3] + x[1]*x[4] + x[2]*x[3] - x[2]*x[4] 5 | ; 6 | 7 | subject to constr1: x[1] + 2*x[2] <= 8; 8 | subject to constr2: 4*x[1] + x[2] <= 12; 9 | subject to constr3: 3*x[1] + 4*x[2] <= 12; 10 | subject to constr4: 2*x[3] + x[4] <= 8; 11 | subject to constr5: x[3] + 2*x[4] <= 8; 12 | subject to constr6: x[3] + x[4] <= 5; 13 | 14 | let x[1] := 0; 15 | let x[2] := 0; 16 | let x[3] := 0; 17 | let x[4] := 0; 18 | 19 | #printf "optimal solution as starting point \n"; 20 | #let x[1] := 0; 21 | #let x[2] := 3; 22 | #let x[3] := 0; 23 | #let x[4] := 4; 24 | -------------------------------------------------------------------------------- /cute/hs045.mod: -------------------------------------------------------------------------------- 1 | var x {i in 1..5} >= 0, <= i; 2 | 3 | minimize obj: 4 | 2 - (prod{i in 1..5} x[i])/120 5 | ; 6 | 7 | #subject to constr1: x[1] + 2*x[2] <= 8; 8 | 9 | let {i in 1..5} x[i] := 0; 10 | -------------------------------------------------------------------------------- /cute/hs046.mod: -------------------------------------------------------------------------------- 1 | var x {1..5}; 2 | 3 | minimize obj: 4 | (x[1]-x[2])^2 + (x[3]-1)^2 + (x[4]-1)^4 + (x[5]-1)^6 5 | ; 6 | 7 | subject to constr1: x[1]^2*x[4] + sin(x[4] - x[5]) = 1; 8 | subject to constr2: x[2] + x[3]^4*x[4]^2 = 2; 9 | 10 | let x[1] := sqrt(2)/2; 11 | let x[2] := 1.75; 12 | let x[3] := 0.5; 13 | let x[4] := 2; 14 | let x[5] := 2; 15 | -------------------------------------------------------------------------------- /cute/hs047.mod: -------------------------------------------------------------------------------- 1 | var x {1..5}; 2 | 3 | minimize obj: 4 | (x[1]-x[2])^2 + (x[2]-x[3])^3 + (x[3]-x[4])^4 + (x[4]-x[5])^4 5 | ; 6 | 7 | subject to constr1: x[1] + x[2]^2 + x[3]^3 = 3; 8 | subject to constr2: x[2] - x[3]^2 + x[4] = 1; 9 | subject to constr3: x[1]*x[5] = 1; 10 | 11 | let x[1] := 2; 12 | let x[2] := sqrt(2); 13 | let x[3] := -1; 14 | let x[4] := 2-sqrt(2); 15 | let x[5] := 1/2; 16 | -------------------------------------------------------------------------------- /cute/hs048.mod: -------------------------------------------------------------------------------- 1 | var x {1..5}; 2 | 3 | minimize obj: 4 | (x[1]-1)^2 + (x[2]-x[3])^2 + (x[4]-x[5])^2 5 | ; 6 | 7 | subject to constr1: sum {i in 1..5} x[i] = 5; 8 | subject to constr2: x[3] - 2*(x[4]+x[5]) = -3; 9 | 10 | let x[1] := 3; 11 | let x[2] := 5; 12 | let x[3] := -3; 13 | let x[4] := 2; 14 | let x[5] := -2; 15 | -------------------------------------------------------------------------------- /cute/hs049.mod: -------------------------------------------------------------------------------- 1 | var x {1..5}; 2 | 3 | minimize obj: 4 | (x[1]-x[2])^2 + (x[3]-1)^2 + (x[4]-1)^4 + (x[5]-1)^6 5 | ; 6 | 7 | subject to constr1: sum {i in 1..4} x[i] + 3*x[4] = 7; 8 | subject to constr2: x[3] + 5*x[5] = 6; 9 | 10 | let x[1] := 10; 11 | let x[2] := 7; 12 | let x[3] := 2; 13 | let x[4] := -3; 14 | let x[5] := 0.8; 15 | -------------------------------------------------------------------------------- /cute/hs050.mod: -------------------------------------------------------------------------------- 1 | var x {1..5}; 2 | 3 | minimize obj: 4 | (x[1]-x[2])^2 + (x[2]-x[3])^2 + (x[3]-x[4])^4 + (x[4]-x[5])^2 5 | ; 6 | 7 | subject to constr1: x[1] + 2*x[2] + 3*x[3] = 6; 8 | subject to constr2: x[2] + 2*x[3] + 3*x[4] = 6; 9 | subject to constr3: x[3] + 2*x[4] + 3*x[5] = 6; 10 | 11 | let x[1] := 35; 12 | let x[2] := -31; 13 | let x[3] := 11; 14 | let x[4] := 5; 15 | let x[5] := -5; 16 | -------------------------------------------------------------------------------- /cute/hs051.mod: -------------------------------------------------------------------------------- 1 | var x {1..5}; 2 | 3 | minimize obj: 4 | (x[1]-x[2])^2 + (x[2]+x[3]-2)^2 + (x[4]-1)^2 + (x[5]-1)^2 5 | ; 6 | 7 | subject to constr1: x[1] + 3*x[2] = 4; 8 | subject to constr2: x[3] + x[4] - 2*x[5] = 0; 9 | subject to constr3: x[2] - x[5] = 0; 10 | 11 | let x[1] := 2.5; 12 | let x[2] := 0.5; 13 | let x[3] := 2; 14 | let x[4] := -1; 15 | let x[5] := 0.5; 16 | -------------------------------------------------------------------------------- /cute/hs052.mod: -------------------------------------------------------------------------------- 1 | var x {1..5}; 2 | 3 | minimize obj: 4 | (4*x[1]-x[2])^2 + (x[2]+x[3]-2)^2 + (x[4]-1)^2 + (x[5]-1)^2 5 | ; 6 | 7 | subject to constr1: x[1] + 3*x[2] = 0; 8 | subject to constr2: x[3] + x[4] - 2*x[5] = 0; 9 | subject to constr3: x[2] - x[5] = 0; 10 | 11 | let x[1] := 2; 12 | let x[2] := 2; 13 | let x[3] := 2; 14 | let x[4] := 2; 15 | let x[5] := 2; 16 | -------------------------------------------------------------------------------- /cute/hs053.mod: -------------------------------------------------------------------------------- 1 | var x {1..5} >= -10, <= 10;; 2 | 3 | minimize obj: 4 | (x[1]-x[2])^2 + (x[2]+x[3]-2)^2 + (x[4]-1)^2 + (x[5]-1)^2 5 | ; 6 | 7 | subject to constr1: x[1] + 3*x[2] = 0; 8 | subject to constr2: x[3] + x[4] - 2*x[5] = 0; 9 | subject to constr3: x[2] - x[5] = 0; 10 | 11 | let x[1] := 2; 12 | let x[2] := 2; 13 | let x[3] := 2; 14 | let x[4] := 2; 15 | let x[5] := 2; 16 | -------------------------------------------------------------------------------- /cute/hs055.mod: -------------------------------------------------------------------------------- 1 | param u {1..6}, default Infinity; 2 | var x {j in 1..6} >= 0, <= u[j]; 3 | 4 | minimize obj: 5 | x[1] + 2*x[2] + 4*x[5] + exp(x[1]*x[4]); 6 | ; 7 | 8 | subject to constr1: x[1] + 2*x[2] + 5*x[5] = 6; 9 | subject to constr2: x[1] + x[2] + x[3] = 3; 10 | subject to constr3: x[4] + x[5] + x[6] = 2; 11 | subject to constr4: x[1] + x[4] = 1; 12 | subject to constr5: x[2] + x[5] = 2; 13 | subject to constr6: x[3] + x[6] = 2; 14 | #subject to constr7: x[1] <= 1; 15 | #subject to constr8: x[4] <= 1; 16 | 17 | data; 18 | 19 | param u := 20 | 1 1 21 | 4 1 22 | ; 23 | 24 | let x[1] := 1; 25 | let x[2] := 2; 26 | let x[3] := 0; 27 | let x[4] := 0; 28 | let x[5] := 0; 29 | let x[6] := 2; 30 | 31 | #printf "optimal solution as starting point \n"; 32 | #let x[1] := 0; 33 | #let x[2] := 4/3; 34 | #let x[3] := 5/3; 35 | #let x[4] := 1; 36 | #let x[5] := 2/3; 37 | #let x[6] := 1/3; 38 | -------------------------------------------------------------------------------- /cute/hs056.mod: -------------------------------------------------------------------------------- 1 | var x {1..7} >= 0; 2 | 3 | param a := asin(sqrt(1/4.2)); 4 | param b := asin(sqrt(5/7.2)); 5 | param c := asin(sqrt(4/7)); 6 | param d := asin(sqrt(2/7)); 7 | 8 | minimize obj: 9 | -x[1]*x[2]*x[3] 10 | ; 11 | 12 | subject to constr1: x[1] - 4.2*sin(x[4])^2 = 0; 13 | subject to constr2: x[2] - 4.2*sin(x[5])^2 = 0; 14 | subject to constr3: x[3] - 4.2*sin(x[6])^2 = 0; 15 | subject to constr4: x[1] + 2*x[2] + 2*x[3] - 7.2*sin(x[7])^2 = 0; 16 | 17 | let x[1] := 1; 18 | let x[2] := 1; 19 | let x[3] := 1; 20 | let x[4] := a; 21 | let x[5] := a; 22 | let x[6] := a; 23 | let x[7] := b; 24 | 25 | #printf "optimal solution as starting point \n"; 26 | #let x[1] := 2.4; 27 | #let x[2] := 1.2; 28 | #let x[3] := 1.2; 29 | #let x[4] := c; 30 | #let x[5] := d; 31 | #let x[6] := d; 32 | #let x[7] := 3.14159/2; 33 | -------------------------------------------------------------------------------- /cute/hs059.mod: -------------------------------------------------------------------------------- 1 | param u {1..2}; 2 | 3 | var x {j in 1..2} >= 0, <= u[j]; 4 | 5 | 6 | minimize obj: 7 | -75.196 + 3.8112*x[1] + 0.0020567*x[1]^3 - 1.0345e-5*x[1]^4 8 | + 6.8306*x[2] - 0.030234*x[1]*x[2] + 1.28134e-3*x[2]*x[1]^2 9 | + 2.266e-7*x[1]^4*x[2] - 0.25645*x[2]^2 + 0.0034604*x[2]^3 - 1.3514e-5*x[2]^4 10 | + 28.106/(x[2] + 1) + 5.2375e-6*x[1]^2*x[2]^2 + 6.3e-8*x[1]^3*x[2]^2 11 | - 7e-10*x[1]^3*x[2]^3 - 3.405e-4*x[1]*x[2]^2 + 1.6638e-6*x[1]*x[2]^3 12 | + 2.8673*exp(0.0005*x[1]*x[2]) - 3.5256e-5*x[1]^3*x[2] 13 | # the last term appears in CUTE but not in H&S 14 | -0.12694*x[1]^2 15 | ; 16 | 17 | subject to constr1: x[1]*x[2] >= 700; 18 | subject to constr2: x[2] - x[1]^2/125 >= 0; 19 | subject to constr3: (x[2] - 50)^2 - 5*(x[1] - 55) >= 0; 20 | 21 | data; 22 | 23 | param u := 24 | 1 75 25 | 2 65 26 | ; 27 | 28 | let x[1] := 90; 29 | let x[2] := 10; 30 | 31 | #printf "optimal solution as starting point \n"; 32 | #let x[1] := 13.55010424; 33 | #let x[2] := 51.66018129; 34 | -------------------------------------------------------------------------------- /cute/hs060.mod: -------------------------------------------------------------------------------- 1 | var x {1..3} >= -10, <= 10; 2 | 3 | 4 | minimize obj: 5 | (x[1] - 1)^2 + (x[1] - x[2])^2 + (x[2] - x[3])^4 6 | ; 7 | 8 | subject to constr1: x[1]*(1 + x[2]^2) + x[3]^4 = 4 + 3*sqrt(2); 9 | 10 | let x[1] := 2; 11 | let x[2] := 2; 12 | let x[3] := 2; 13 | 14 | #printf "optimal solution as starting point \n"; 15 | #let x[1] := 1.104859024; 16 | #let x[2] := 1.196674194; 17 | #let x[3] := 1.535262257; 18 | -------------------------------------------------------------------------------- /cute/hs061.mod: -------------------------------------------------------------------------------- 1 | var x {1..3}; 2 | 3 | 4 | minimize obj: 5 | 4*x[1]^2 + 2*x[2]^2 + 2*x[3]^2 - 33*x[1] + 16*x[2] - 24*x[3] 6 | ; 7 | 8 | subject to constr1: 3*x[1] - 2*x[2]^2 = 7; 9 | subject to constr2: 4*x[1] - x[3]^2 = 11; 10 | 11 | let x[1] := 0; 12 | let x[2] := 0; 13 | let x[3] := 0; 14 | 15 | #printf "optimal solution as starting point \n"; 16 | #let x[1] := 5.326770157; 17 | #let x[2] := -2.118998639; 18 | #let x[3] := 3.210464239; 19 | -------------------------------------------------------------------------------- /cute/hs062.mod: -------------------------------------------------------------------------------- 1 | var x {1..3} >=0, <= 1; 2 | 3 | 4 | minimize obj: 5 | -32.174*(255*log((x[1]+x[2]+x[3]+0.03)/(0.09*x[1] + x[2] + x[3] + 0.03)) 6 | +280*log((x[2]+x[3]+0.03)/(0.07*x[2] + x[3] + 0.03)) 7 | +290*log((x[3]+0.03)/(0.13*x[3] + 0.03))) 8 | ; 9 | 10 | subject to constr1: x[1] + x[2] + x[3] = 1; 11 | 12 | let x[1] := 0.7; 13 | let x[2] := 0.2; 14 | let x[3] := 0.1; 15 | 16 | #printf "optimal solution as starting point \n"; 17 | #let x[1] := 0.6178126908; 18 | #let x[2] := 0.328202223; 19 | #let x[3] := 0.5398508606e-1; 20 | -------------------------------------------------------------------------------- /cute/hs063.mod: -------------------------------------------------------------------------------- 1 | var x {1..3} >=0; 2 | 3 | minimize obj: 4 | 1000 - x[1]^2 - 2*x[2]^2 - x[3]^2 - x[1]*x[2] - x[1]*x[3] 5 | ; 6 | 7 | subject to constr1: 8*x[1] + 14*x[2] + 7*x[3] = 56; 8 | subject to constr2: x[1]^2 + x[2]^2 + x[3]^2 = 25; 9 | 10 | let x[1] := 2; 11 | let x[2] := 2; 12 | let x[3] := 2; 13 | 14 | #printf "optimal solution as starting point \n"; 15 | #let x[1] := 3.512118414; 16 | #let x[2] := 0.2169881741; 17 | #let x[3] := 3.552174034; 18 | -------------------------------------------------------------------------------- /cute/hs064.mod: -------------------------------------------------------------------------------- 1 | var x {1..3} >= 1.0e-5; 2 | 3 | minimize obj: 4 | 5*x[1] + 50000/x[1] + 20*x[2] + 72000/x[2] + 10*x[3] + 144000/x[3] 5 | ; 6 | 7 | subject to constr1: 4/x[1] + 32/x[2] + 120/x[3] <= 1; 8 | 9 | let x[1] := 1; 10 | let x[2] := 1; 11 | let x[3] := 1; 12 | 13 | #printf "optimal solution as starting point \n"; 14 | #let x[1] := 108.7347175; 15 | #let x[2] := 85.12613942; 16 | #let x[3] := 204.3247078; 17 | -------------------------------------------------------------------------------- /cute/hs065.mod: -------------------------------------------------------------------------------- 1 | var x {1..3}; 2 | 3 | minimize obj: 4 | (x[1] - x[2])^2 + (x[1] + x[2] - 10)^2/9 + (x[3] - 5)^2 5 | ; 6 | 7 | subject to constr1: x[1]^2 + x[2]^2 + x[3]^2 <= 48; 8 | subject to constr2: -4.5 <= x[1] <= 4.5; 9 | subject to constr3: -4.5 <= x[2] <= 4.5; 10 | subject to constr4: -5 <= x[3] <= 5; 11 | 12 | let x[1] := -5; 13 | let x[2] := 5; 14 | let x[3] := 0; 15 | 16 | #printf "optimal solution as starting point \n"; 17 | #let x[1] := 3.650461821; 18 | #let x[2] := 3.65046168; 19 | #let x[3] := 4.6204170507; 20 | -------------------------------------------------------------------------------- /cute/hs066.mod: -------------------------------------------------------------------------------- 1 | var x {1..3}; 2 | 3 | minimize obj: 4 | 0.2*x[3] - 0.8*x[1] 5 | ; 6 | 7 | subject to constr1: x[2] - exp(x[1]) >= 0; 8 | subject to constr2: x[3] - exp(x[2]) >= 0; 9 | subject to constr3: 0 <= x[1] <= 100; 10 | subject to constr4: 0 <= x[2] <= 100; 11 | subject to constr5: 0 <= x[3] <= 10; 12 | 13 | let x[1] := 0; 14 | let x[2] := 1.05; 15 | let x[3] := 2.9; 16 | 17 | #printf "optimal solution as starting point \n"; 18 | #let x[1] := 0.1841264879; 19 | #let x[2] := 1.202167873; 20 | #let x[3] := 3.327322322; 21 | -------------------------------------------------------------------------------- /cute/hs068.mod: -------------------------------------------------------------------------------- 1 | function myerf; 2 | 3 | param l {1..4}; 4 | param u {1..4}; 5 | 6 | var x {j in 1..4} >= l[j], <= u[j]; 7 | 8 | param a := 0.0001; 9 | param b := 1; 10 | param d := 1; 11 | param n := 24; 12 | 13 | minimize obj: 14 | ( a*n - (b*(exp(x[1])-1) - x[3])*x[4]/(exp(x[1]) - 1 + x[4]) )/x[1] 15 | ; 16 | 17 | subject to constr1: 18 | x[3] - 2*myerf(-x[2]) = 0; 19 | subject to constr2: 20 | x[4] = myerf(-x[2] + d*sqrt(n)) + myerf(-x[2] - d*sqrt(n)); 21 | 22 | data; 23 | 24 | param l := 25 | 1 0.0001 26 | 2 0 27 | 3 0 28 | 4 0 29 | ; 30 | 31 | param u := 32 | 1 100 33 | 2 100 34 | 3 2 35 | 4 2 36 | ; 37 | 38 | let x[1] := 1; 39 | let x[2] := 1; 40 | let x[3] := 1; 41 | let x[4] := 1; 42 | 43 | #printf "optimal solution as starting point \n"; 44 | #let x[1] := 0.06785874; 45 | #let x[2] := 3.6461717; 46 | #let x[3] := 0.00026617; 47 | #let x[4] := 0.8948622; 48 | -------------------------------------------------------------------------------- /cute/hs069.mod: -------------------------------------------------------------------------------- 1 | function myerf; 2 | 3 | param l {1..4}; 4 | param u {1..4}; 5 | 6 | var x {j in 1..4} >= l[j], <= u[j]; 7 | 8 | param a := 0.1; 9 | param b := 1000; 10 | param d := 1; 11 | param n := 4; 12 | 13 | minimize obj: 14 | ( a*n - (b*(exp(x[1])-1) - x[3])*x[4]/(exp(x[1]) - 1 + x[4]) )/x[1] ; 15 | 16 | subject to constr1: 17 | x[3] - 2*myerf(-x[2]) = 0; 18 | subject to constr2: 19 | x[4] = myerf(-x[2] + d*sqrt(n)) + myerf(-x[2] - d*sqrt(n)); 20 | 21 | data; 22 | 23 | param l := 24 | 1 0.0001 25 | 2 0 26 | 3 0 27 | 4 0 28 | ; 29 | 30 | param u := 31 | 1 100 32 | 2 100 33 | 3 2 34 | 4 2 35 | ; 36 | 37 | let x[1] := 1; 38 | let x[2] := 1; 39 | let x[3] := 1; 40 | let x[4] := 1; 41 | 42 | #printf "optimal solution as starting point \n"; 43 | #let x[1] := 0.02937141; 44 | #let x[2] := 1.1902534; 45 | #let x[3] := 0.23394676; 46 | #let x[4] := 0.7916678; 47 | -------------------------------------------------------------------------------- /cute/hs071.mod: -------------------------------------------------------------------------------- 1 | var x {1..4} >= 1, <= 5; 2 | 3 | minimize obj: 4 | x[1]*x[4]*(x[1] + x[2] + x[3]) + x[3] 5 | ; 6 | 7 | subject to constr1: prod {i in 1..4} x[i] >= 25; 8 | subject to constr2: sum {i in 1..4} x[i]^2 = 40; 9 | 10 | let x[1] := 1; 11 | let x[2] := 5; 12 | let x[3] := 5; 13 | let x[4] := 1; 14 | 15 | #printf "optimal solution as starting point \n"; 16 | #let x[1] := 1; 17 | #let x[2] := 4.742994; 18 | #let x[3] := 3.8211503; 19 | #let x[4] := 1.3794082; 20 | -------------------------------------------------------------------------------- /cute/hs072.mod: -------------------------------------------------------------------------------- 1 | param a {1..2, 1..4}; 2 | param b {1..2}; 3 | 4 | var x {1..4} >= 0.001; 5 | 6 | minimize obj: 7 | 1 + sum {j in 1..4} x[j] 8 | ; 9 | 10 | subject to constr {i in 1..2}: sum {j in 1..4} a[i,j]/x[j] <= b[i]; 11 | subject to ub {j in 1..4}: x[j] <= (5-j)*1e5; 12 | 13 | let x[1] := 1; 14 | let x[2] := 1; 15 | let x[3] := 1; 16 | let x[4] := 1; 17 | 18 | #printf "optimal solution as starting point \n"; 19 | #let x[1] := 193.4071; 20 | #let x[2] := 179.5475; 21 | #let x[3] := 185.0186; 22 | #let x[4] := 168.7062; 23 | 24 | data; 25 | 26 | param a: 1 2 3 4 := 27 | 1 4 2.25 1 0.25 28 | 2 0.16 0.36 0.64 0.64 29 | ; 30 | 31 | param b := 32 | 1 0.0401 33 | 2 0.010085 34 | ; 35 | -------------------------------------------------------------------------------- /cute/hs073.mod: -------------------------------------------------------------------------------- 1 | var x {1..4} >= 0; 2 | 3 | minimize obj: 4 | 24.55*x[1] + 26.75*x[2] + 39*x[3] + 40.50*x[4] 5 | ; 6 | 7 | subject to constr1: 2.3*x[1] + 5.6*x[2] + 11.1*x[3] + 1.3*x[4] >= 5; 8 | subject to constr2: 12*x[1] + 11.9*x[2] + 41.8*x[3] + 52.1*x[4] 9 | >= 21 + 10 | 1.645*sqrt(0.28*x[1]^2 + 0.19*x[2]^2 + 20.5*x[3]^2 + 0.62*x[4]^2); 11 | subject to constr3: sum {j in 1..4} x[j] = 1; 12 | 13 | let x[1] := 1; 14 | let x[2] := 1; 15 | let x[3] := 1; 16 | let x[4] := 1; 17 | 18 | #printf "optimal solution as starting point \n"; 19 | #let x[1] := 0.6355216; 20 | #let x[2] := -0.12e-11; 21 | #let x[3] := 0.3127019; 22 | #let x[4] := 0.5177655; 23 | 24 | data; 25 | -------------------------------------------------------------------------------- /cute/hs076.mod: -------------------------------------------------------------------------------- 1 | var x {j in 1..4} >= 0; 2 | 3 | minimize obj: 4 | x[1]^2 + 0.5*x[2]^2 + x[3]^2 + 0.5*x[4]^2 - x[1]*x[3] + x[3]*x[4] 5 | - x[1] - 3*x[2] + x[3] - x[4] 6 | ; 7 | 8 | subject to constr1: x[1] + 2*x[2] + x[3] + x[4] <= 5; 9 | subject to constr2: 3*x[1] + x[2] + 2*x[3] - x[4] <= 4; 10 | subject to constr3: x[2] + 4*x[3] >= 1.5; 11 | 12 | data; 13 | 14 | let x[1] := 0.5; 15 | let x[2] := 0.5; 16 | let x[3] := 0.5; 17 | let x[4] := 0.5; 18 | 19 | #printf "optimal solution as starting point \n"; 20 | #let x[1] := 0.2727273; 21 | #let x[2] := 2.090909; 22 | #let x[3] := -0.26e-10; 23 | #let x[4] := 0.5454545; 24 | 25 | data; 26 | -------------------------------------------------------------------------------- /cute/hs077.mod: -------------------------------------------------------------------------------- 1 | var x {1..5}; 2 | 3 | minimize obj: 4 | (x[1]-1)^2 + (x[1] - x[2])^2 + (x[3]-1)^2 + (x[4]-1)^4 + (x[5]-1)^6 5 | ; 6 | 7 | subject to constr1: x[1]^2*x[4] + sin(x[4]-x[5]) = 2*sqrt(2); 8 | subject to constr2: x[2] + x[3]^4*x[4]^2 = 8 + sqrt(2); 9 | 10 | data; 11 | 12 | let x[1] := 2; 13 | let x[2] := 2; 14 | let x[3] := 2; 15 | let x[4] := 2; 16 | let x[5] := 2; 17 | 18 | #printf "optimal solution as starting point \n"; 19 | #let x[1] := 1.166172; 20 | #let x[2] := 1.182111; 21 | #let x[3] := 1.380257; 22 | #let x[4] := 1.506036; 23 | #let x[5] := 0.6109203; 24 | 25 | data; 26 | -------------------------------------------------------------------------------- /cute/hs078.mod: -------------------------------------------------------------------------------- 1 | var x {1..5}; 2 | 3 | minimize obj: 4 | prod {j in 1..5} x[j] 5 | ; 6 | 7 | subject to constr1: sum {j in 1..5} x[j]^2 = 10; 8 | subject to constr2: x[2]*x[3] - 5*x[4]*x[5] = 0; 9 | subject to constr3: x[1]^3 + x[2]^3 = -1; 10 | 11 | data; 12 | 13 | let x[1] := -2; 14 | let x[2] := 1.5; 15 | let x[3] := 2; 16 | let x[4] := -1; 17 | let x[5] := -1; 18 | 19 | #printf "optimal solution as starting point \n"; 20 | #let x[1] := -1.717142; 21 | #let x[2] := 1.595708; 22 | #let x[3] := 1.827248; 23 | #let x[4] := -0.7636429; 24 | #let x[5] := -0.7636435; 25 | 26 | data; 27 | -------------------------------------------------------------------------------- /cute/hs079.mod: -------------------------------------------------------------------------------- 1 | var x {1..5}; 2 | 3 | minimize obj: 4 | (x[1]-1)^2 + (x[1]-x[2])^2 + (x[2]-x[3])^2 + (x[3]-x[4])^4 + (x[4]-x[5])^4 5 | ; 6 | 7 | subject to constr1: x[1] + x[2]^2 + x[3]^3 = 2 + 3*sqrt(2); 8 | subject to constr2: x[2] - x[3]^2 + x[4] = -2 + 2*sqrt(2); 9 | subject to constr3: x[1]*x[5] = 2; 10 | 11 | data; 12 | 13 | let x[1] := 2; 14 | let x[2] := 2; 15 | let x[3] := 2; 16 | let x[4] := 2; 17 | let x[5] := 2; 18 | 19 | #printf "optimal solution as starting point \n"; 20 | #let x[1] := 1.191127; 21 | #let x[2] := 1.362603; 22 | #let x[3] := 1.472818; 23 | #let x[4] := 1.635017; 24 | #let x[5] := 1.679081; 25 | 26 | data; 27 | -------------------------------------------------------------------------------- /cute/hs080.mod: -------------------------------------------------------------------------------- 1 | param l {1..5}; 2 | param u {1..5}; 3 | 4 | var x {j in 1..5} >= l[j], <= u[j]; 5 | 6 | minimize obj: 7 | exp( prod {j in 1..5} x[j] ) 8 | ; 9 | 10 | subject to constr1: sum {j in 1..5} x[j]^2 = 10; 11 | subject to constr2: x[2]*x[3] - 5*x[4]*x[5] = 0; 12 | subject to constr3: x[1]^3 + x[2]^3 = -1; 13 | 14 | data; 15 | 16 | param l := 17 | 1 -2.3 18 | 2 -2.3 19 | 3 -3.2 20 | 4 -3.2 21 | 5 -3.2 22 | ; 23 | 24 | param u := 25 | 1 2.3 26 | 2 2.3 27 | 3 3.2 28 | 4 3.2 29 | 5 3.2 30 | ; 31 | 32 | let x[1] := -2; 33 | let x[2] := 2; 34 | let x[3] := 2; 35 | let x[4] := -1; 36 | let x[5] := -1; 37 | 38 | #printf "optimal solution as starting point \n"; 39 | #let x[1] := -1.717143; 40 | #let x[2] := 1.595709; 41 | #let x[3] := 1.827247; 42 | #let x[4] := -0.7636413; 43 | #let x[5] := -0.7636450; 44 | 45 | data; 46 | -------------------------------------------------------------------------------- /cute/hs081.mod: -------------------------------------------------------------------------------- 1 | param l {1..5}; 2 | param u {1..5}; 3 | 4 | var x {j in 1..5} >= l[j], <= u[j]; 5 | 6 | minimize obj: 7 | exp( prod {j in 1..5} x[j] ) - 0.5*(x[1]^3 + x[2]^3 + 1)^2 8 | ; 9 | 10 | subject to constr1: sum {j in 1..5} x[j]^2 = 10; 11 | subject to constr2: x[2]*x[3] - 5*x[4]*x[5] = 0; 12 | subject to constr3: x[1]^3 + x[2]^3 = -1; 13 | 14 | data; 15 | 16 | param l := 17 | 1 -2.3 18 | 2 -2.3 19 | 3 -3.2 20 | 4 -3.2 21 | 5 -3.2 22 | ; 23 | 24 | param u := 25 | 1 2.3 26 | 2 2.3 27 | 3 3.2 28 | 4 3.2 29 | 5 3.2 30 | ; 31 | 32 | let x[1] := -2; 33 | let x[2] := 2; 34 | let x[3] := 2; 35 | let x[4] := -1; 36 | let x[5] := -1; 37 | 38 | #printf "optimal solution as starting point \n"; 39 | #let x[1] := -1.717142; 40 | #let x[2] := 1.159571; 41 | #let x[3] := 1.827248; 42 | #let x[4] := -0.7636474; 43 | #let x[5] := -0.7636390; 44 | 45 | data; 46 | -------------------------------------------------------------------------------- /cute/hs093.mod: -------------------------------------------------------------------------------- 1 | var x {1..6} >= 0; 2 | 3 | minimize obj: 4 | 0.0204*x[1]*x[4]*(x[1] + x[2] + x[3]) + 5 | 0.0187*x[2]*x[3]*(x[1] + 1.57*x[2] + x[4]) + 6 | 0.0607*x[1]*x[4]*x[5]^2*(x[1] + x[2] + x[3]) + 7 | 0.0437*x[2]*x[3]*x[6]^2*(x[1] + 1.57*x[2] + x[4]) 8 | ; 9 | 10 | subject to constr1: 11 | 0.001* prod {j in 1..6} x[j] >= 2.07; 12 | 13 | subject to constr2: 14 | 0.00062*x[1]*x[4]*x[5]^2*(x[1] + x[2] + x[3]) + 15 | 0.00058*x[2]*x[3]*x[6]^2*(x[1] + 1.57*x[2] + x[4]) 16 | <= 1; 17 | 18 | data; 19 | 20 | let x[1] := 5.54; 21 | let x[2] := 4.4; 22 | let x[3] := 12.02; 23 | let x[4] := 11.82; 24 | let x[5] := 0.702; 25 | let x[6] := 0.852; 26 | 27 | #printf "optimal solution as starting point \n"; 28 | #let x[1] := 5.332666; 29 | #let x[2] := 4.656744; 30 | #let x[3] := 10.43299; 31 | #let x[4] := 12.08230; 32 | #let x[5] := 0.7526074; 33 | #let x[6] := 0.87865084; 34 | -------------------------------------------------------------------------------- /cute/hs100.mod: -------------------------------------------------------------------------------- 1 | var x {1..7}; 2 | 3 | minimize obj: 4 | (x[1]-10)^2 + 5*(x[2]-12)^2 + x[3]^4 + 3*(x[4]-11)^2 + 10*x[5]^6 5 | + 7*x[6]^2 + x[7]^4 - 4*x[6]*x[7] - 10*x[6] - 8*x[7] 6 | ; 7 | 8 | subject to constr1: 2*x[1]^2 + 3*x[2]^4 + x[3] + 4*x[4]^2 + 5*x[5] <= 127; 9 | subject to constr2: 7*x[1] + 3*x[2] + 10*x[3]^2 + x[4] - x[5] <= 282; 10 | subject to constr3: 23*x[1] + x[2]^2 + 6*x[6]^2 - 8*x[7] <= 196; 11 | subject to constr4: -4*x[1]^2 - x[2]^2 + 3*x[1]*x[2] -2*x[3]^2 - 5*x[6] 12 | +11*x[7] >= 0; 13 | 14 | data; 15 | 16 | let x[1] := 1; 17 | let x[2] := 2; 18 | let x[3] := 0; 19 | let x[4] := 4; 20 | let x[5] := 0; 21 | let x[6] := 1; 22 | let x[7] := 1; 23 | 24 | #printf "optimal solution as starting point \n"; 25 | #let x[1] := 2.330499; 26 | #let x[2] := 1.951372; 27 | #let x[3] := -0.4775414; 28 | #let x[4] := 4.365726; 29 | #let x[5] := -0.6244870; 30 | #let x[6] := 1.038131; 31 | #let x[7] := 1.594227; 32 | -------------------------------------------------------------------------------- /cute/hs104.mod: -------------------------------------------------------------------------------- 1 | var x{1..8} >=.1 <=10; 2 | 3 | minimize obj: 4 | .4*x[1]^.67*x[7]^-.67+.4*x[2]^.67*x[8]^-.67+10-x[1]-x[2]; 5 | 6 | s.t. c1: 1-.0588*x[5]*x[7]-.1*x[1]>=0; 7 | s.t. c2: 1-.0588*x[6]*x[8]-.1*x[1]-.1*x[2]>=0; 8 | s.t. c3: 1-4*x[3]/x[5]-2/(x[3]^.71*x[5])-.0588*x[7]/x[3]^1.3>=0; 9 | s.t. c4: 1-4*x[4]/x[6]-2/(x[4]^.71*x[6])-.0588*x[8]/x[4]^1.3>=0; 10 | s.t. c5: .4*x[1]^.67*x[7]^-.67+.4*x[2]^.67*x[8]^-.67+10-x[1]-x[2]>=.1; 11 | s.t. c6: .4*x[1]^.67*x[7]^-.67+.4*x[2]^.67*x[8]^-.67+10-x[1]-x[2]<=4.2; 12 | 13 | data; 14 | 15 | let x[1] := 6 ; 16 | let x[2] := 3 ; 17 | let x[3] := .4; 18 | let x[4] := .2; 19 | let x[5] := 6 ; 20 | let x[6] := 6 ; 21 | let x[7] := 1 ; 22 | let x[8] := .5; 23 | -------------------------------------------------------------------------------- /cute/hs110.mod: -------------------------------------------------------------------------------- 1 | var x {1..10} >= 2.001, <= 9.999; 2 | 3 | minimize obj: 4 | sum {j in 1..10} ( log(x[j]-2)^2 + log(10-x[j])^2 ) 5 | - 6 | (prod {j in 1..10} x[j])^0.2 7 | ; 8 | 9 | let {j in 1..10} x[j] := 9; 10 | -------------------------------------------------------------------------------- /cute/hs111.mod: -------------------------------------------------------------------------------- 1 | var x {1..10} >= -100, <= 100; 2 | 3 | param c {1..10}; 4 | 5 | minimize obj: 6 | sum {j in 1..10} exp(x[j])*(c[j] + x[j] - log(sum {k in 1..10} exp(x[k]))); 7 | 8 | subject to cons1: 9 | exp(x[1]) + 2*exp(x[2]) + 2*exp(x[3]) + exp(x[6]) + exp(x[10]) = 2; 10 | 11 | subject to cons2: 12 | exp(x[4]) + 2*exp(x[5]) + exp(x[6]) + exp(x[7]) = 1; 13 | 14 | subject to cons3: 15 | exp(x[3]) + exp(x[7]) + exp(x[8]) + 2*exp(x[9]) + exp(x[10]) = 1; 16 | 17 | data; 18 | 19 | param c := 20 | 1 -6.089 21 | 2 -17.164 22 | 3 -34.054 23 | 4 -5.914 24 | 5 -24.721 25 | 6 -14.986 26 | 7 -24.100 27 | 8 -10.708 28 | 9 -26.662 29 | 10 -22.179 30 | ; 31 | 32 | let {j in 1..10} x[j] := -2.3; 33 | -------------------------------------------------------------------------------- /cute/hs112.mod: -------------------------------------------------------------------------------- 1 | var x {1..10} >= 1.0e-6; 2 | 3 | param c {1..10}; 4 | 5 | minimize obj: 6 | sum {j in 1..10} x[j]*(c[j] 7 | + log(x[j]/sum {k in 1..10} x[k]) ); 8 | 9 | subject to cons1: 10 | x[1] + 2*x[2] + 2*x[3] + x[6] + x[10] = 2; 11 | 12 | subject to cons2: 13 | x[4] + 2*x[5] + x[6] + x[7] = 1; 14 | 15 | subject to cons3: 16 | x[3] + x[7] + x[8] + 2*x[9] + x[10] = 1; 17 | 18 | data; 19 | 20 | param c := 21 | 1 -6.089 22 | 2 -17.164 23 | 3 -34.054 24 | 4 -5.914 25 | 5 -24.721 26 | 6 -14.986 27 | 7 -24.100 28 | 8 -10.708 29 | 9 -26.662 30 | 10 -22.179 31 | ; 32 | 33 | let {j in 1..10} x[j] := 0.1; 34 | -------------------------------------------------------------------------------- /cute/hs113.mod: -------------------------------------------------------------------------------- 1 | var x {1..10}; 2 | 3 | minimize obj: 4 | x[1]^2+x[2]^2+x[1]*x[2]-14*x[1]-16*x[2]+(x[3]-10)^2+4*(x[4]-5)^2 5 | +(x[5]-3)^2+2*(x[6]-1)^2+5*x[7]^2+7*(x[8]-11)^2+2*(x[9]-10)^2 6 | +(x[10]-7)^2+45; 7 | 8 | s.t. c1: 105-4*x[1]-5*x[2]+3*x[7]-9*x[8]>=0; 9 | s.t. c2: -10*x[1]+8*x[2]+17*x[7]-2*x[8]>=0; 10 | s.t. c3: 8*x[1]-2*x[2]-5*x[9]+2*x[10]+12>=0; 11 | s.t. c4: -3*(x[1]-2)^2-4*(x[2]-3)^2-2*x[3]^2+7*x[4]+120>=0; 12 | s.t. c5: -5*x[1]^2-8*x[2]-(x[3]-6)^2+2*x[4]+40>=0; 13 | s.t. c6: -.5*(x[1]-8)^2-2*(x[2]-4)^2-3*x[5]^2+x[6]+30>=0; 14 | s.t. c7: -x[1]^2-2*(x[2]-2)^2+2*x[1]*x[2]-14*x[5]+6*x[6]>=0; 15 | s.t. c8: 3*x[1]-6*x[2]-12*(x[9]-8)^2+7*x[10]>=0; 16 | 17 | data; 18 | 19 | let x[1] := 2; 20 | let x[2] := 3; 21 | let x[3] := 5; 22 | let x[4] := 5; 23 | let x[5] := 1; 24 | let x[6] := 2; 25 | let x[7] := 7; 26 | let x[8] := 3; 27 | let x[9] := 6; 28 | let x[10] := 10; 29 | -------------------------------------------------------------------------------- /cute/hs3mod.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: problem 3 in 13 | # W. Hock and K. Schittkowski, 14 | # "Test examples for nonlinear programming codes", 15 | # Lectures Notes in Economics and Mathematical Systems 187, Springer 16 | # Verlag, Heidelberg, 1981. 17 | 18 | # SIF input: A.R. Conn March 1990 19 | 20 | # classification QBR2-AN-2-0 21 | 22 | param xinit{1..2}; 23 | var x{i in 1..2} := xinit[i]; 24 | 25 | minimize f: 26 | x[2]+(-x[1]+x[2])^2; 27 | subject to cons1: 28 | x[2] >= 0; 29 | 30 | data; 31 | param xinit:= 1 10.0 2 1.0; 32 | -------------------------------------------------------------------------------- /cute/humps.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # Ph. Toint, private communication, 1997. 14 | 15 | # SDIF input: Ph. Toint, May 1997. 16 | 17 | # classification SUR2-AN-2-0 18 | 19 | param zeta := 20.0; 20 | var x:=-506.0; 21 | var y:=-506.2; 22 | 23 | minimize f: 24 | 0.05*(x^2+y^2) + (sin(zeta*x)*sin(zeta*y))^2; 25 | -------------------------------------------------------------------------------- /cute/indef.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification OUR2-AN-V-0 13 | 14 | param n := 1000; 15 | param alpha := 0.5; 16 | 17 | var x{i in 1..n} := i/(n+1); 18 | 19 | minimize f: 20 | sum {i in 1..n} (x[i]) + 21 | sum {i in 2..n-1} alpha*cos(2*x[i]-x[n]-x[1]); 22 | -------------------------------------------------------------------------------- /cute/jensmp.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: Problem 6 in 13 | # J.J. More', B.S. Garbow and K.E. Hillstrom, 14 | # "Testing Unconstrained Optimization Software", 15 | # ACM Transactions on Mathematical Software, vol. 7(1), pp. 17-41, 1981. 16 | 17 | # SIF input: Ph. Toint, Dec 1989. 18 | 19 | # classification OUR2-AN-2-0 20 | 21 | var x1 := 0.3; 22 | var x2 := 0.4; 23 | 24 | minimize f: 25 | sum {i in 1..10} (2+2*i-(exp(i*x1)+exp(i*x2)))^2; 26 | -------------------------------------------------------------------------------- /cute/kiwcresc.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # K.C. Kiwiel, 14 | # "Methods of Descent for Nondifferentiable Optimization" 15 | # Lectures Notes in Mathematics 1133, Springer Verlag, 1985. 16 | 17 | # SIF input: Ph. Toint, Nov 1993. 18 | 19 | # classification LQR2-AN-3-2 20 | 21 | param xinit{1..2}; 22 | var x{i in 1..2} := xinit[i]; 23 | var u; 24 | minimize f: 25 | u; 26 | subject to cons1: 27 | -u+x[2]-1+x[1]^2+(x[2]-1)^2 <= 0; 28 | subject to cons2: 29 | -u+x[2]+1-x[1]^2-(x[2]-1)^2 <= 0; 30 | 31 | data; 32 | param xinit:= 1 -1.5 2 2.0; 33 | -------------------------------------------------------------------------------- /cute/liarwhd.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # G. Li, 14 | # "The secant/finite difference algorithm for solving sparse 15 | # nonlinear systems of equations", 16 | # SIAM Journal on Optimization, (to appear), 1990. 17 | 18 | # SIF input: Ph. Toint, Aug 1990. 19 | 20 | # classification SUR2-AN-V-0 21 | 22 | param N:=10000; 23 | var x{1..N} := 4.0; 24 | 25 | minimize f: 26 | sum {i in 1..N} 4*(-x[1]+x[i]^2)^2 + sum {i in 1..N} (x[i]-1.0)^2; 27 | -------------------------------------------------------------------------------- /cute/loghairy.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # Ph. Toint, private communication, 14 | 15 | # SIF input: Ph. Toint, April 1997. 16 | 17 | # classification OUR2-AN-2-0 18 | 19 | param hlength:=30; 20 | param cslope:=100; 21 | 22 | var x1 := -500; 23 | var x2 := -700; 24 | 25 | minimize f: 26 | log( (100+sin(7*x1)^2*cos(7*x2)^2*hlength + 27 | cslope*sqrt(0.01+(x1-x2)^2) + cslope*sqrt(0.01+x1^2))/100) 28 | ; 29 | -------------------------------------------------------------------------------- /cute/logros.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # Ph. Toint, private communication, 1991. 14 | 15 | # SDIF input: Ph. Toint, June 1993. 16 | 17 | # classification OBR2-AN-2-0 18 | 19 | var x:=-1.2, >= 0; 20 | var y:=1.0, >= 0; 21 | 22 | minimize f: 23 | log(1+10000*(y-x^2)^2+(1-x)^2); 24 | -------------------------------------------------------------------------------- /cute/makela1.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # M.M. Makela, 14 | # "Nonsmooth optimization", 15 | # Ph.D. thesis, Jyvaskyla University, 1990 16 | 17 | # SIF input: Ph. Toint, Nov 1993. 18 | 19 | # classification LQR2-AN-3-2 20 | 21 | var x{1..2} := -0.5; 22 | var u; 23 | 24 | minimize f: 25 | u; 26 | subject to cons1: 27 | -u-x[1]-x[2] <= 0; 28 | subject to cons2: 29 | -u-x[1]-x[2]-1.0+x[1]^2+x[2]^2 <= 0; 30 | -------------------------------------------------------------------------------- /cute/makela2.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # M.M. Makela, 14 | # "Nonsmooth optimization", 15 | # Ph.D. thesis, Jyvaskyla University, 1990 16 | 17 | # SIF input: Ph. Toint, Nov 1993. 18 | 19 | # classification LQR2-AN-3-3 20 | 21 | param xinit{1..2}; 22 | var x{i in 1..2} := xinit[i]; 23 | var u; 24 | 25 | minimize f: 26 | u; 27 | subject to cons1: 28 | -u+x[1]^2+x[2]^2 <= 0; 29 | subject to cons2: 30 | x[1]^2+x[2]^2-u-40*x[1]-10*x[2]+40 <= 0; 31 | subject to cons3: 32 | x[1]^2+x[2]^2-u-10*x[1]-20*x[2]+60 <= 0; 33 | 34 | data; 35 | param xinit:= 1 -1.0 2 5.0; 36 | -------------------------------------------------------------------------------- /cute/makela3.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # M.M. Makela, 14 | # "Nonsmooth optimization", 15 | # Ph.D. thesis, Jyvaskyla University, 1990 16 | 17 | # SIF input: Ph. Toint, Nov 1993. 18 | 19 | # classification LQR2-AN-21-20 20 | 21 | var x{i in 1..20} := if (i <= 10) then i else -i; 22 | var u; 23 | 24 | minimize f: 25 | u; 26 | subject to cons{i in 1..20}: 27 | -u+x[i]^2 <= 0; 28 | -------------------------------------------------------------------------------- /cute/maratosb.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # Ph. Toint. 14 | 15 | # SIF input: Ph. Toint, June 1990. 16 | 17 | # classification QUR2-AN-2-0 18 | 19 | param invp := 0.000001; 20 | param xinit{1..2}; 21 | var x{i in 1..2} := xinit[i]; 22 | 23 | minimize f: 24 | x[1]+(x[1]^2+x[2]^2-1)^2/invp; 25 | 26 | data; 27 | param xinit:= 1 0 2 0; 28 | -------------------------------------------------------------------------------- /cute/matrix2.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification QOR2-AY-6-2 13 | 14 | var x11 >= 0, := 1; 15 | var x12 := 1; 16 | var x22 >= 0, := 1; 17 | var y11 <= 0, := 1; 18 | var y12 := 1; 19 | var y22 <= 0, := 1; 20 | 21 | minimize f: 22 | (x11-y11)^2 + 2*(x12-y12)^2 + (x22-y22)^2; 23 | subject to cons1: 24 | x11*x22-x12^2 >= 0; 25 | subject to cons2: 26 | y11*y22-y12^2<= 0; 27 | -------------------------------------------------------------------------------- /cute/mccormck.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: Problem 29 in 13 | # Ph. L. Toint, 14 | # "Test problems for partially separable optimization and results 15 | # for the routine PSPMIN", 16 | # Report 83/4, FUNDP (Namur, B), 1983. 17 | 18 | # SIF input: Ph. Toint, Dec 1989. 19 | 20 | # classification OBR2-AY-V-0 21 | 22 | param N:=50000; 23 | var x{1..N} >= -1.5, <= 3.0; 24 | 25 | minimize f: 26 | sum {i in 1..N-1} (-1.5*x[i]+2.5*x[i+1]+1.0+(x[i]-x[i+1])^2+sin(x[i]+x[i+1])); 27 | -------------------------------------------------------------------------------- /cute/mdhole.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # Ph. Toint, private communication. 14 | 15 | # SIF input: Ph. Toint, March 1991. 16 | 17 | # classification OBR2-AN-2-0 18 | 19 | var x:=10.0, >= 0; 20 | var y:=10.0; 21 | 22 | minimize f: 23 | ((-y+sin(x))^2)/0.01 + x; 24 | -------------------------------------------------------------------------------- /cute/mexhat.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # A.A. Brown and M. Bartholomew-Biggs, 14 | # "Some effective methods for unconstrained optimization based on 15 | # the solution of ordinary differential equations", 16 | # Technical Report 178, Numerical Optimization Centre, Hatfield 17 | # Polytechnic, (Hatfield, UK), 1987. 18 | 19 | # SIF input: Ph. Toint, June 1990. 20 | 21 | # classification OUR2-AN-2-0 22 | 23 | param p := 10000; 24 | var x1 := 0.86; 25 | var x2 := 0.72; 26 | 27 | minimize f: 28 | - 2*(x1-1)^2 29 | + p*(-0.02 + (x2-x1^2)^2/p + (x1-1)^2)^2 30 | ; 31 | -------------------------------------------------------------------------------- /cute/mifflin1.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # M.M. Makela, 14 | # "Nonsmooth optimization", 15 | # Ph.D. thesis, Jyvaskyla University, 1990 16 | 17 | # SIF input: Ph. Toint, Nov 1993. 18 | 19 | # classification LQR2-AN-3-2 20 | 21 | param xinit{1..2}; 22 | var x{i in 1..2}:=xinit[i]; 23 | var u; 24 | minimize f: 25 | u; 26 | subject to cons1: 27 | -u-x[1]-1.0+x[1]^2+x[2]^2 <= 0; 28 | subject to cons2: 29 | -u-x[1]<=0; 30 | 31 | data; 32 | param xinit:= 1 0.8 2 0.6; 33 | -------------------------------------------------------------------------------- /cute/mifflin2.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # M.M. Makela, 14 | # "Nonsmooth optimization", 15 | # Ph.D. thesis, Jyvaskyla University, 1990 16 | 17 | # SIF input: Ph. Toint, Nov 1993. 18 | 19 | # classification LQR2-AN-3-2 20 | 21 | var x{1..2} := -1.0; 22 | var u; 23 | minimize f: 24 | u; 25 | subject to cons1: 26 | -u-x[1]-3.75+3.75*(x[1]^2+x[2]^2) <= 0; 27 | subject to cons2: 28 | -u-x[1]-0.25+0.25*(x[1]^2+x[2]^2) <= 0; 29 | -------------------------------------------------------------------------------- /cute/minsurf.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification OXR2-MY-64-0 13 | 14 | param p:=7; 15 | var x{1..p+1,1..p+1}; 16 | var A{i in 1..p, j in 1..p} = (x[i,j]-x[i+1,j+1])^2; 17 | var B{i in 1..p, j in 1..p} = (x[i,j+1]-x[i+1,j])^2; 18 | minimize f: 19 | sum {i in 1..p} sum {j in 1..p} sqrt( (1+0.5*A[i,j]*p^2+0.5*B[i,j]*p^2) )/p^2; 20 | subject to cons1{j in 1..p+1}: 21 | x[1,j] = 1.0; 22 | subject to cons2{j in 1..p+1}: 23 | x[p+1,j] = 1.0; 24 | subject to cons3{j in 1..p+1}: 25 | x[j,1] = 1.0; 26 | subject to cons4{j in 1..p+1}: 27 | x[j,p+1] = 1.0; 28 | -------------------------------------------------------------------------------- /cute/nasty.mod: -------------------------------------------------------------------------------- 1 | # 2 | #************************** 3 | # SET UP THE INITIAL DATA * 4 | #************************** 5 | # Problem : 6 | # ********* 7 | # Source: a very simple box-constrained quadratic 8 | # SIF input: Nick Gould, June 1996 9 | # classification QUR2-AN-2-0 10 | # Solution 11 | param one := 1.0; 12 | param theta := 1.0e10; 13 | param beta := (((1.0) / (1.0e10)) * ((1.0) / (1.0e10))) * ((1.0) / (1.0e10)); 14 | param beta2 := ((1.0) / (1.0e10)) * ((1.0) / (1.0e10)); 15 | 16 | var x1 := 1.0e-30; 17 | var x2 := 1.0; 18 | 19 | minimize obj: 20 | 0.5*(1.0e10*x1)*(1.0e10*x1) + 0.5*(x2)*(x2); 21 | -------------------------------------------------------------------------------- /cute/ncvxbqp1.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification QBR2-AN-V-0 13 | 14 | param N:=10000; 15 | param M:=N/2; 16 | param Nplus :=N/4; 17 | var x{i in 1..N} <= 10.0, >= 0.1, := 0.5; 18 | 19 | minimize f: 20 | sum {i in 1..Nplus} 0.5*i*(x[i]+x[ ((2*i-1) mod N) + 1] + x[ ((3*i-1) mod N) +1 ] )^2 - 21 | sum {i in Nplus+1..N} 0.5*i*(x[i]+x[ ((2*i-1) mod N) + 1] + x[ ((3*i-1) mod N) +1 ] )^2 ; 22 | -------------------------------------------------------------------------------- /cute/ncvxbqp2.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification QBR2-AN-V-0 13 | 14 | param N:=10000; 15 | param M:=N/2; 16 | param Nplus :=N/2; 17 | var x{1..N} <= 10.0, >= 0.1, := 0.5; 18 | 19 | minimize f: 20 | sum {i in 1..Nplus} 0.5*i*(x[i]+x[ ((2*i-1) mod N) + 1] + x[ ((3*i-1) mod N) +1 ] )^2 - 21 | sum {i in Nplus+1..N} 0.5*i*(x[i]+x[ ((2*i-1) mod N) + 1] + x[ ((3*i-1) mod N) +1 ] )^2 ; 22 | -------------------------------------------------------------------------------- /cute/ncvxbqp3.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification QBR2-AN-V-0 13 | 14 | param N:=10000; 15 | param M:=N/2; 16 | param Nplus :=3*N/4; 17 | var x{1..N} <= 10.0, >= 0.1, := 0.5; 18 | 19 | minimize f: 20 | sum {i in 1..Nplus} 0.5*i*(x[i]+x[ ((2*i-1) mod N) + 1] + x[ ((3*i-1) mod N) +1 ] )^2 - 21 | sum {i in Nplus+1..N} 0.5*i*(x[i]+x[ ((2*i-1) mod N) + 1] + x[ ((3*i-1) mod N) +1 ] )^2 ; 22 | -------------------------------------------------------------------------------- /cute/ncvxqp1.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification QLR2-AN-V-V 13 | 14 | param N:=1000; 15 | param M:=N/2; 16 | param NPLUS:=N/4; 17 | 18 | var x{1..N} >= 0.1, <= 10.0, := 0.5; 19 | 20 | minimize f: 21 | sum {i in 1..NPLUS} (x[i]+x[((2*i-1) mod N)+1] 22 | +x[((3*i-1) mod N)+1])^2*i/2 - 23 | sum {i in NPLUS+1..N} (x[i]+x[((2*i-1) mod N)+1] 24 | +x[((3*i-1) mod N)+1])^2*i/2 ; 25 | subject to cons1{i in 1..M}: 26 | x[i]+2*x[((4*i-1) mod N)+1] + 3*x[((5*i-1) mod N)+1] - 6.0 = 0; 27 | -------------------------------------------------------------------------------- /cute/ncvxqp2.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification QLR2-AN-V-V 13 | 14 | param N:=1000; 15 | param M:=N/2; 16 | param NPLUS:=N/2; 17 | 18 | var x{1..N} >= 0.1, <= 10.0, := 0.5; 19 | 20 | minimize f: 21 | sum {i in 1..NPLUS} (x[i]+x[(2*i-1)-((2*i-1) div N)*N+1] 22 | +x[(3*i-1)-((3*i-1) div N)*N+1])^2*i/2 - 23 | sum {i in NPLUS+1..N} (x[i]+x[(2*i-1)-((2*i-1) div N)*N+1] 24 | +x[(3*i-1)-((3*i-1) div N)*N+1])^2*i/2 ; 25 | subject to cons1{i in 1..M}: 26 | x[i]+2*x[(4*i-1)-((4*i-1) div N)*N+1] + 3*x[(5*i-1)-((5*i-1) 27 | div N)*N+1] = 6.0 ; 28 | -------------------------------------------------------------------------------- /cute/ncvxqp3.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification QLR2-AN-V-V 13 | 14 | param N:=1000; 15 | param M:=N/2; 16 | param NPLUS:=3*N/4; 17 | 18 | var x{1..N} >= 0.1, <= 10.0, := 0.5; 19 | 20 | minimize f: 21 | sum {i in 1..NPLUS} (x[i]+x[(2*i-1) mod N + 1] 22 | +x[(3*i-1) mod N + 1])^2*i/2 - 23 | sum {i in NPLUS+1..N} (x[i]+x[(2*i-1) mod N + 1] 24 | +x[(3*i-1) mod N + 1])^2*i/2 ; 25 | subject to cons1{i in 1..M}: 26 | x[i]+2*x[(4*i-1) mod N + 1] + 3*x[(5*i-1) 27 | mod N + 1] = 6.0 ; 28 | -------------------------------------------------------------------------------- /cute/ncvxqp4.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification QLR2-AN-V-V 13 | 14 | param N:=1000; 15 | param M:=N/4; 16 | param NPLUS:=N/4; 17 | 18 | var x{1..N} >= 0.1, <= 10.0, := 0.5; 19 | 20 | minimize f: 21 | sum {i in 1..NPLUS} (x[i]+x[(2*i-1)-((2*i-1) div N)*N+1] 22 | +x[(3*i-1)-((3*i-1) div N)*N+1])^2*i/2 - 23 | sum {i in NPLUS+1..N} (x[i]+x[(2*i-1)-((2*i-1) div N)*N+1] 24 | +x[(3*i-1)-((3*i-1) div N)*N+1])^2*i/2 ; 25 | subject to cons1{i in 1..M}: 26 | x[i]+2*x[(4*i-1)-((4*i-1) div N)*N+1] + 3*x[(5*i-1)-((5*i-1) 27 | div N)*N+1] - 6.0 = 0; 28 | -------------------------------------------------------------------------------- /cute/ncvxqp5.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification QLR2-AN-V-V 13 | 14 | param N:=1000; 15 | param M:=N/4; 16 | param NPLUS:=N/2; 17 | 18 | var x{1..N} >= 0.1, <= 10.0, := 0.5; 19 | 20 | minimize f: 21 | sum {i in 1..NPLUS} (x[i]+x[(2*i-1)-((2*i-1) div N)*N+1] 22 | +x[(3*i-1)-((3*i-1) div N)*N+1])^2*i/2 - 23 | sum {i in NPLUS+1..N} (x[i]+x[(2*i-1)-((2*i-1) div N)*N+1] 24 | +x[(3*i-1)-((3*i-1) div N)*N+1])^2*i/2 ; 25 | subject to cons1{i in 1..M}: 26 | x[i]+2*x[(4*i-1)-((4*i-1) div N)*N+1] + 3*x[(5*i-1)-((5*i-1) 27 | div N)*N+1] - 6.0 = 0; 28 | -------------------------------------------------------------------------------- /cute/ncvxqp6.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification QLR2-AN-V-V 13 | 14 | param N:=1000; 15 | param M:=N/4; 16 | param NPLUS:=3*N/4; 17 | 18 | var x{1..N} >= 0.1, <= 10.0, := 0.5; 19 | 20 | minimize f: 21 | sum {i in 1..NPLUS} (x[i]+x[(2*i-1)-((2*i-1) div N)*N+1] 22 | +x[(3*i-1)-((3*i-1) div N)*N+1])^2*i/2 - 23 | sum {i in NPLUS+1..N} (x[i]+x[(2*i-1)-((2*i-1) div N)*N+1] 24 | +x[(3*i-1)-((3*i-1) div N)*N+1])^2*i/2 ; 25 | subject to cons1{i in 1..M}: 26 | x[i]+2*x[(4*i-1)-((4*i-1) div N)*N+1] + 3*x[(5*i-1)-((5*i-1) 27 | div N)*N+1] - 6.0 = 0; 28 | -------------------------------------------------------------------------------- /cute/ncvxqp7.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification QLR2-AN-V-V 13 | 14 | param N:=1000; 15 | param M:=3*N/4; 16 | param NPLUS:=N/4; 17 | 18 | var x{1..N} >= 0.1, <= 10.0, := 0.5; 19 | 20 | minimize f: 21 | sum {i in 1..NPLUS} (x[i]+x[(2*i-1)-((2*i-1) div N)*N+1] 22 | +x[(3*i-1)-((3*i-1) div N)*N+1])^2*i/2 - 23 | sum {i in NPLUS+1..N} (x[i]+x[(2*i-1)-((2*i-1) div N)*N+1] 24 | +x[(3*i-1)-((3*i-1) div N)*N+1])^2*i/2 ; 25 | subject to cons1{i in 1..M}: 26 | x[i]+2*x[(4*i-1)-((4*i-1) div N)*N+1] + 3*x[(5*i-1)-((5*i-1) 27 | div N)*N+1] - 6.0 = 0; 28 | -------------------------------------------------------------------------------- /cute/ncvxqp8.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification QLR2-AN-V-V 13 | 14 | param N:=1000; 15 | param M:=3*N/4; 16 | param NPLUS:=N/2; 17 | 18 | var x{1..N} >= 0.1, <= 10.0, := 0.5; 19 | 20 | minimize f: 21 | sum {i in 1..NPLUS} (x[i]+x[(2*i-1)-((2*i-1) div N)*N+1] 22 | +x[(3*i-1)-((3*i-1) div N)*N+1])^2*i/2 - 23 | sum {i in NPLUS+1..N} (x[i]+x[(2*i-1)-((2*i-1) div N)*N+1] 24 | +x[(3*i-1)-((3*i-1) div N)*N+1])^2*i/2 ; 25 | subject to cons1{i in 1..M}: 26 | x[i]+2*x[(4*i-1)-((4*i-1) div N)*N+1] + 3*x[(5*i-1)-((5*i-1) 27 | div N)*N+1] = 6.0 ; 28 | -------------------------------------------------------------------------------- /cute/ncvxqp9.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification QLR2-AN-V-V 13 | 14 | param N:=1000; 15 | param M:=3*N/4; 16 | param NPLUS:=3*N/4; 17 | 18 | var x{1..N} >= 0.1, <= 10.0, := 0.5; 19 | 20 | minimize f: 21 | sum {i in 1..NPLUS} (x[i]+x[(2*i-1)-((2*i-1) div N)*N+1] 22 | +x[(3*i-1)-((3*i-1) div N)*N+1])^2*i/2 - 23 | sum {i in NPLUS+1..N} (x[i]+x[(2*i-1)-((2*i-1) div N)*N+1] 24 | +x[(3*i-1)-((3*i-1) div N)*N+1])^2*i/2 ; 25 | subject to cons1{i in 1..M}: 26 | x[i]+2*x[(4*i-1)-((4*i-1) div N)*N+1] + 3*x[(5*i-1)-((5*i-1) 27 | div N)*N+1] = 6.0 ; 28 | -------------------------------------------------------------------------------- /cute/noncvxu2.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification OUR2-AN-V-0 13 | 14 | param n := 1000; 15 | var x {j in 1..n} := j; 16 | 17 | minimize obj: 18 | sum {j in 1..n} ( (x[j] + x[((3*j-2) mod n)+1] + x[((7*j-3) mod n)+1])^2 + 19 | 4*cos(x[j] + x[((3*j-2) mod n)+1] + x[((7*j-3) mod n)+1]) ); 20 | -------------------------------------------------------------------------------- /cute/nondia.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # D. Shanno, 14 | # " On Variable Metric Methods for Sparse Hessians II: the New 15 | # Method", 16 | # MIS Tech report 27, University of Arizona (Tucson, UK), 1978. 17 | 18 | # See also Buckley #37 (p. 76) and Toint #15. 19 | 20 | # SIF input: Ph. Toint, Dec 1989. 21 | 22 | # classification SUR2-AN-V-0 23 | 24 | param N:=10000; 25 | var x{1..N} := -1; 26 | 27 | minimize f: 28 | (x[1]-1)^2 29 | + sum {i in 2..N} 100*(x[1]-x[i-1]^2)^2; 30 | -------------------------------------------------------------------------------- /cute/nondquar.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: problem 57 in 13 | # A.R. Conn, N.I.M. Gould, M. Lescrenier and Ph.L. Toint, 14 | # "Performance of a multi-frontal scheme for partially separable 15 | # optimization" 16 | # Report 88/4, Dept of Mathematics, FUNDP (Namur, B), 1988. 17 | 18 | # SIF input: Ph. Toint, Dec 1989. 19 | 20 | # classification OUR2-AN-V-0 21 | 22 | param N := 10000; 23 | var x{i in 1..N} := if (i mod 2 = 0) then -1 else 1; 24 | 25 | minimize f: 26 | sum {i in 1..N-2} (x[i]+x[i+1]+x[N])^4 + (x[1]-x[2])^2 + (x[N-1]+x[N])^2; 27 | -------------------------------------------------------------------------------- /cute/nonmsqrt.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # Ph. Toint 14 | 15 | # SIF input: Ph. Toint, Dec 1989. 16 | 17 | # classification SUR2-AN-V-0 18 | 19 | param P := 3; 20 | param N := P^2; 21 | param B{i in 1..P, j in 1..P} := if (i==3 && j==1) then 0 else sin ( 22 | ((i-1)*P + j)^2 ); 23 | param A{i in 1..P, j in 1..P} := sum {k in 1..P} B[i,k]*B[k,j]; 24 | 25 | var x{i in 1..P, j in 1..P} := if (i==3 && j==1) then -0.8*sin(((i-1)*P + j)^2 ) else 0.2*B[i,j]; 26 | 27 | minimize f: 28 | sum {i in 1..P, j in 1..P} (sum {t in 1..P} x[i,t]*x[i,j] 29 | -A[i,j])^2; 30 | -------------------------------------------------------------------------------- /cute/nonscomp.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # M. Lescrenier, 14 | # "Towards the use of supercomputers for large scale nonlinear 15 | # partially separable optimization", 16 | # PhD Thesis, FUNDP (Namur, B), 1989. 17 | 18 | # SIF input: Ph. Toint, May 1990. 19 | 20 | # classification SBR2-AN-V-0 21 | 22 | param N := 10000; 23 | var x{i in 1..N} := 3, >= if (i mod 3 == 0) then 1 else -100, <= 100; 24 | 25 | minimize f: 26 | (x[1] - 1)^2 27 | + sum {i in 2..N} 4*(x[i]-x[i-1]^2)^2 28 | ; 29 | -------------------------------------------------------------------------------- /cute/nuffield_continuum.mod: -------------------------------------------------------------------------------- 1 | param c := 5; 2 | 3 | var a >=0, <=1; 4 | var b >=0, <=1; 5 | 6 | maximize foo: (c+1)*((1-b)^2+(3-2*a))/4 7 | - c*((1-b)^2+(1-a)^2)/4 8 | - 3*( 9 | a^3/24 + (1-a)*(1-(1-b)^2)/4 10 | # + (1-b)^3/3 + (1-b)^2*(b-a)/4 11 | + (1-b)^2*(1-(a+b)/2)/2 - (1-b)^3/6 12 | ); 13 | 14 | s.t. alessb: a <= b; 15 | 16 | let a:=0.03; 17 | let b:=0.10; 18 | -------------------------------------------------------------------------------- /cute/penalty1.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: Problem 23 in 13 | # J.J. More', B.S. Garbow and K.E. Hillstrom, 14 | # "Testing Unconstrained Optimization Software", 15 | # ACM Transactions on Mathematical Software, vol. 7(1), pp. 17-41, 1981. 16 | 17 | # See also Buckley #181 (p. 79). 18 | 19 | # SIF input: Ph. Toint, Dec 1989. 20 | 21 | # classification SUR2-AN-V-0 22 | 23 | param N:=1000; 24 | param M:=N+1; 25 | 26 | var x{i in 1..N} := i; 27 | 28 | param a := 10^-5; 29 | 30 | minimize f: 31 | sum {i in 1..N} a*(x[i]-1)^2 + ( sum {j in 1..N} x[j]^2 - 1/4 )^2; 32 | -------------------------------------------------------------------------------- /cute/pfit1.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification NOR2-AN-3-3 13 | 14 | param cf := -8.0; 15 | param cg := -18-(2/3); 16 | param ch := -23-(1/9); 17 | 18 | var a:=1.0; 19 | var r:=0.0; 20 | var h:=1.0; 21 | 22 | minimize f: 23 | (-0.5*(a*(a+1)*r*h^2)+a*r*h-r*(1-(1+h)^-a)-cf)^2 + 24 | (-a*(a+1)*r*h^2+a*r*h*(1-(1+h)^-(a+1))-cg)^2 + 25 | (-a*(a+1)*r*h^2*(1-(1+h)^-(a+2))-ch)^2; 26 | -------------------------------------------------------------------------------- /cute/pfit1ls.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification SUR2-AN-3-0 13 | 14 | param cf := -8.0; 15 | param cg := -18-(2/3); 16 | param ch := -23-(1/9); 17 | 18 | var a:=1.0; 19 | var r:=0.0; 20 | var h:=1.0; 21 | 22 | minimize f: 23 | (-0.5*(a*(a+1)*r*h^2)+a*r*h-r*(1-(1+h)^-a)-cf)^2 + 24 | (-a*(a+1)*r*h^2+a*r*h*(1-(1+h)^-(a+1))-cg)^2 + 25 | (-a*(a+1)*r*h^2*(1-(1+h)^-(a+2))-ch)^2; 26 | -------------------------------------------------------------------------------- /cute/pfit2.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification NOR2-AN-3-3 13 | 14 | param cf := -26-(2/3); 15 | param cg := -60-(4/9); 16 | param ch := -71-(1/9); 17 | 18 | var a:=1.0; 19 | var r:=0.0; 20 | var h:=1.0; 21 | 22 | minimize f: 23 | (-0.5*(a*(a+1)*r*h^2)+a*r*h-r*(1-(1+h)^-a)-cf)^2 + 24 | (-a*(a+1)*r*h^2+a*r*h*(1-(1+h)^-(a+1))-cg)^2 + 25 | (-a*(a+1)*r*h^2*(1-(1+h)^-(a+2))-ch)^2; 26 | -------------------------------------------------------------------------------- /cute/pfit2ls.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification SUR2-AN-3-0 13 | 14 | param cf := -26-(2/3); 15 | param cg := -60-(4/9); 16 | param ch := -71-(1/9); 17 | 18 | var a:=1.0; 19 | var r:=0.0; 20 | var h:=1.0; 21 | 22 | minimize f: 23 | (-0.5*(a*(a+1)*r*h^2)+a*r*h-r*(1-(1+h)^-a)-cf)^2 + 24 | (-a*(a+1)*r*h^2+a*r*h*(1-(1+h)^-(a+1))-cg)^2 + 25 | (-a*(a+1)*r*h^2*(1-(1+h)^-(a+2))-ch)^2; 26 | -------------------------------------------------------------------------------- /cute/pfit3.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification NOR2-AN-3-3 13 | 14 | param cf := -56-(8/9); 15 | param cg := -126-(2/9); 16 | param ch := -143-(407/999); 17 | 18 | var a:=1.0; 19 | var r:=0.0; 20 | var h:=1.0; 21 | 22 | minimize f: 23 | (-0.5*(a*(a+1)*r*h^2)+a*r*h-r*(1-(1+h)^-a)-cf)^2 + 24 | (-a*(a+1)*r*h^2+a*r*h*(1-(1+h)^-(a+1))-cg)^2 + 25 | (-a*(a+1)*r*h^2*(1-(1+h)^-(a+2))-ch)^2; 26 | -------------------------------------------------------------------------------- /cute/pfit3ls.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification SUR2-AN-3-0 13 | 14 | param cf := -56-(8/9); 15 | param cg := -126-(2/9); 16 | param ch := -143-(407/999); 17 | 18 | var a:=1.0; 19 | var r:=0.0; 20 | var h:=1.0; 21 | 22 | minimize f: 23 | (-0.5*(a*(a+1)*r*h^2)+a*r*h-r*(1-(1+h)^-a)-cf)^2 + 24 | (-a*(a+1)*r*h^2+a*r*h*(1-(1+h)^-(a+1))-cg)^2 + 25 | (-a*(a+1)*r*h^2*(1-(1+h)^-(a+2))-ch)^2; 26 | -------------------------------------------------------------------------------- /cute/pfit4.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification NOR2-AN-3-3 13 | 14 | param cf := -98.9629629629; 15 | param cg := -216.098765432; 16 | param ch := -239.670781893; 17 | 18 | var a:=1.0; 19 | var r:=0.0; 20 | var h:=1.0; 21 | 22 | minimize f: 23 | (-0.5*(a*(a+1)*r*h^2)+a*r*h-r*(1-(1+h)^-a)-cf)^2 + 24 | (-a*(a+1)*r*h^2+a*r*h*(1-(1+h)^-(a+1))-cg)^2 + 25 | (-a*(a+1)*r*h^2*(1-(1+h)^-(a+2))-ch)^2; 26 | -------------------------------------------------------------------------------- /cute/pfit4ls.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification SUR2-AN-3-0 13 | 14 | param cf := -98.9629629629; 15 | param cg := -216.098765432; 16 | param ch := -239.670781893; 17 | 18 | var a:=1.0; 19 | var r:=0.0; 20 | var h:=1.0; 21 | 22 | minimize f: 23 | (-0.5*(a*(a+1)*r*h^2)+a*r*h-r*(1-(1+h)^-a)-cf)^2 + 24 | (-a*(a+1)*r*h^2+a*r*h*(1-(1+h)^-(a+1))-cg)^2 + 25 | (-a*(a+1)*r*h^2*(1-(1+h)^-(a+2))-ch)^2; 26 | -------------------------------------------------------------------------------- /cute/polak1.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # E. Polak, D.H. Mayne and J.E. Higgins, 14 | # "Superlinearly convergent algorithm for min-max problems" 15 | # JOTA 69, pp. 407-439, 1991. 16 | 17 | # SIF input: Ph. Toint, Nov 1993. 18 | 19 | # classification LOR2-AN-3-2 20 | 21 | param xinit{1..2}; 22 | var x{i in 1..2} := xinit[i]; 23 | var u; 24 | 25 | minimize f: 26 | u; 27 | subject to cons1: 28 | -u+exp(0.001*x[1]^2+(x[2]-1)^2) <= 0; 29 | subject to cons2: 30 | -u+exp(0.001*x[1]^2+(x[2]+1)^2) <= 0; 31 | 32 | data; 33 | param xinit:= 1 50.0 2 0.05; 34 | -------------------------------------------------------------------------------- /cute/polak5.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # E. Polak, D.H. Mayne and J.E. Higgins, 14 | # "Superlinearly convergent algorithm for min-max problems" 15 | # JOTA 69, pp. 407-439, 1991. 16 | 17 | # SIF input: Ph. Toint, Nov 1993. 18 | 19 | # classification LOR2-AN-3-2 20 | 21 | var x{1..2} := 0.1; 22 | var u; 23 | 24 | minimize f: 25 | u; 26 | subject to cons1: 27 | -u+3*x[1]^2+50*(x[1]-x[2]^4-1)^2 <= 0; 28 | subject to cons2: 29 | -u+3*x[1]^2+50*(x[1]-x[2]^4+1)^2 <= 0; 30 | -------------------------------------------------------------------------------- /cute/powell20.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: a generalization of problem 20 in 13 | # M. J. D. Powell 14 | # "On the quadratic progamming algorithm of Goldfarb and Idnani", 15 | # Mathematical Programmimg Study 25 (1985) 46-61. 16 | 17 | # SIF input: Nick Gould, August 1994. 18 | 19 | # classification QLR2-AN-V-V 20 | 21 | param N:=1000; 22 | var x{i in 1..N}:=if ( (i mod 2) == 1) then 0 else -0.5-i; 23 | 24 | minimize f: 25 | 0.5*sum {i in 1..N} x[i]^2; 26 | subject to cons1{k in 1..N-1}: 27 | x[k+1]-x[k] >= -0.5+(-1)^k*k; 28 | subject to cons2: 29 | x[1]-x[N] >= N-0.5; 30 | -------------------------------------------------------------------------------- /cute/powellsq.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # M.J.D. Powell, 14 | # " A hybrid method for nonlinear equations", 15 | # In P. Rabinowitz(ed.) "Numerical Methods for Nonlinear Algebraic 16 | # Equations", Gordon and Breach, 1970. 17 | 18 | # See also Buckley#217 (p.84.) 19 | 20 | # classification NOR2-AN-2-2 21 | 22 | param xinit{1..2}; 23 | var x{i in 1..2} := xinit[i]; 24 | 25 | minimize f: 0; 26 | subject to cons1: 27 | (x[1]^2) = 0; 28 | subject to cons2: 29 | (10*x[1]/(x[1]+0.1)+2*x[2]^2) = 0; 30 | 31 | data; 32 | param xinit:= 1 3 2 1; 33 | -------------------------------------------------------------------------------- /cute/power.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # S.S. Oren, 14 | # Self-scaling variable metric algorithms, 15 | # Part II: implementation and experiments" 16 | # Management Science 20(5):863-874, 1974. 17 | 18 | # See also Buckley#179 (p. 83) 19 | 20 | # SIF input: Ph. Toint, Dec 1989. 21 | 22 | # classification OUR2-AN-V-0 23 | 24 | param N:=1000; 25 | var x{1..N} := 1.0; 26 | 27 | minimize f: 28 | sum {i in 1..N} (i*x[i])^2; 29 | -------------------------------------------------------------------------------- /cute/probpenl.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: problem 46 in 13 | # Ph.L. Toint, 14 | # "Test problems for partially separable optimization and results 15 | # for the routine PSPMIN", 16 | # Report 83/4, Department of Mathematics, FUNDP (Namur, B), 1983. 17 | 18 | # SIF input: Ph. Toint, Dec 1989. 19 | 20 | # classification OBR2-AN-V-0 21 | 22 | param N := 500; 23 | 24 | var x{1..N} >= -5, <= 5, := 0.5; 25 | 26 | minimize f: 27 | sum {i in 1..N-1} (x[i]+x[i+1])*0.0001*exp(-x[i]*x[i+1])/N 28 | + 100*(sum {i in 1..N} x[i] - 1)^2; 29 | -------------------------------------------------------------------------------- /cute/pspdoc.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: problem 47 in 13 | # Ph.L. Toint, 14 | # "Test problems for partially separable optimization and results 15 | # for the routine PSPMIN", 16 | # Report 83/4, Department of Mathematics, FUNDP (Namur, B), 1983. 17 | 18 | # SIF input: Ph. Toint, Dec 1989. 19 | 20 | # classification SBR2-AY-4-0 21 | 22 | param N:=4; 23 | param NGS := N-2; 24 | 25 | var x{1..N} := 3; 26 | 27 | minimize f: 28 | sum {i in 1..NGS} sqrt(x[i]^2+(x[i+1]-x[i+2])^2+1) ; 29 | subject to cons1: 30 | x[1] <= -1; 31 | -------------------------------------------------------------------------------- /cute/qrtquad.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification OBR2-MN-V-0 13 | 14 | param N := 120; 15 | param M := 10; 16 | 17 | var x{1..N} := 0.0; 18 | 19 | minimize f: 20 | sum {i in 1..M} ((i/M)*(x[i]*x[i+1])^4-10*i*x[i]) 21 | + sum {i in M+1..N-1} (4*x[i]^2+2*x[N]^2+x[i]*x[N]-10*i*x[i]); 22 | subject to cons{i in 1..M}: 23 | 0.0 <= x[i] <= 10.0; 24 | -------------------------------------------------------------------------------- /cute/quartc.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: problem 157 (p. 87) in 13 | # A.R. Buckley, 14 | # "Test functions for unconstrained minimization", 15 | # TR 1989CS-3, Mathematics, statistics and computing centre, 16 | # Dalhousie University, Halifax (CDN), 1989. 17 | 18 | # SIF input: Ph. Toint, March 1991. 19 | 20 | # classification OUR2-AN-V-0 21 | 22 | param N:=10000; 23 | var x{1..N} := 2.0; 24 | 25 | minimize f: 26 | sum {i in 1..N} (x[i]-i)^4; 27 | -------------------------------------------------------------------------------- /cute/qudlin.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification QBR2-AN-V-V 13 | 14 | param N:=12; 15 | param M:=6; 16 | var x{1..N} >= 0.0, <= 10.0; 17 | minimize f: 18 | sum {i in 1..N} -i*10*x[i] + sum {i in 1..M} x[i]*x[i+1]; 19 | -------------------------------------------------------------------------------- /cute/rosenbr.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: problem 1 in 13 | # J.J. More', B.S. Garbow and K.E. Hillstrom, 14 | # "Testing Unconstrained Optimization Software", 15 | # ACM Transactions on Mathematical Software, vol. 7(1), pp. 17-41, 1981. 16 | 17 | # SIF input: Ph. Toint, Dec 1989, Corrected July 1993. 18 | 19 | # classification SUR2-AN-2-0 20 | 21 | param xinit{1..2}; 22 | var x{i in 1..2} := xinit[i]; 23 | 24 | minimize f: 25 | (x[2]-x[1]^2)^2/0.01+(x[1]-1)^2; 26 | 27 | data; 28 | param xinit:= 1 -1.2 2 1.0; 29 | -------------------------------------------------------------------------------- /cute/s332.mod: -------------------------------------------------------------------------------- 1 | param N := 2; 2 | param pi := 4*atan(1); # 3.1415; 3 | var x{1..N}; 4 | param t{i in 1..100} := pi*(1/3+(i-1)/180); 5 | #var pmax = max {i in 1..100} ((180/pi)*atan((1/t[i]-x[1])/(log(t[i])+x[2]))); 6 | 7 | minimize f: 8 | (pi/3.6)*sum {i in 1..100} ((log(t[i])+x[2]*sin(t[i])+x[1]*cos(t[i]))^2 + 9 | (log(t[i])+x[2]*cos(t[i])-x[1]*sin(t[i]))^2); 10 | 11 | subject to cons1 {i in 1..100}: 12 | -30 <= (180/pi)*atan((1/t[i]-x[1])/(log(t[i])+x[2])) <= 30; 13 | 14 | subject to cons2{i in 1..2}: 15 | 0 <= x[i] <= 1.5; 16 | 17 | data; 18 | var x:= 19 | 1 0.75 20 | 2 0.75; 21 | -------------------------------------------------------------------------------- /cute/s368.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # P. Wolfe, 14 | # "Explicit solution of an optimization problem", 15 | # Mathematical Programming 2, 258-260, 1972. 16 | 17 | # SIF input: Nick Gould, Oct 1992. 18 | 19 | # See also Schittkowski #368 (for N = 8) 20 | 21 | # classification OBR2-MN-V-0 22 | 23 | param n := 100; 24 | 25 | var x{1..n} <= 1.0, >= 0.0; 26 | 27 | minimize f: 28 | sum {i in 1..n, j in 1..n} (-x[i]^2*x[j]^4) + 29 | sum {i in 1..n, j in 1..n} (x[i]^3*x[j]^3); 30 | -------------------------------------------------------------------------------- /cute/scosine.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # N. Gould, private communication. 14 | 15 | # SIF input: N. Gould, Nov 1997 16 | 17 | # classification OUR2-AN-V-0 18 | 19 | param N:=10000; 20 | param scal := 12.0; 21 | param scale{i in 1..N} := exp((i-1)*scal/(N-1)); 22 | var x{i in 1..N} := 1.0/scale[i]; 23 | 24 | minimize f: 25 | sum {i in 1..N-1} 26 | cos(-0.5*scale[i+1]*x[i+1]+scale[i]^2*x[i]^2); 27 | -------------------------------------------------------------------------------- /cute/scurly10.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: Nick Gould 13 | 14 | # SIF input: Nick Gould, September 1997. 15 | 16 | # classification SUR2-AN-V-0 17 | 18 | param N:=10000; 19 | param K:=10; 20 | param sc := 12.0; 21 | param scale{i in 1..N} := exp((i-1)*sc/(N-1)); 22 | var x{i in 1..N} := 0.0001*i*scale[i]/(N+1); 23 | var y{i in 1..N-K} = sum {j in i..i+K} x[j]*scale[j]; 24 | var z{i in N-K+1..N} = sum {j in i..N} x[j]*scale[j]; 25 | 26 | minimize f: 27 | sum {i in 1..N-K} (y[i]*(y[i]*(y[i]^2-20)-0.1)) + sum {i in N-K+1..N} (z[i]*(z[i]*(z[i]^2-20)-0.1)); 28 | -------------------------------------------------------------------------------- /cute/scurly20.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: Nick Gould 13 | 14 | # SIF input: Nick Gould, September 1997. 15 | 16 | # classification SUR2-AN-V-0 17 | 18 | param N:=10000; 19 | param K:=20; 20 | param sc := 12.0; 21 | param scale{i in 1..N} := exp((i-1)*sc/(N-1)); 22 | var x{i in 1..N} := 0.0001*i*scale[i]/(N+1); 23 | var y{i in 1..N-K} = sum {j in i..i+K} x[j]*scale[j]; 24 | var z{i in N-K+1..N} = sum {j in i..N} x[j]*scale[j]; 25 | 26 | minimize f: 27 | sum {i in 1..N-K} (y[i]*(y[i]*(y[i]^2-20)-0.1)) + sum {i in N-K+1..N} (z[i]*(z[i]*(z[i]^2-20)-0.1)); 28 | -------------------------------------------------------------------------------- /cute/scurly30.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: Nick Gould 13 | 14 | # SIF input: Nick Gould, September 1997. 15 | 16 | # classification SUR2-AN-V-0 17 | 18 | param N:=10000; 19 | param K:=30; 20 | param sc := 12.0; 21 | param scale{i in 1..N} := exp((i-1)*sc/(N-1)); 22 | var x{i in 1..N} := 0.0001*i*scale[i]/(N+1); 23 | var y{i in 1..N-K} = sum {j in i..i+K} x[j]*scale[j]; 24 | var z{i in N-K+1..N} = sum {j in i..N} x[j]*scale[j]; 25 | 26 | minimize f: 27 | sum {i in 1..N-K} (y[i]*(y[i]*(y[i]^2-20)-0.1)) + sum {i in N-K+1..N} (z[i]*(z[i]*(z[i]^2-20)-0.1)); 28 | -------------------------------------------------------------------------------- /cute/sensors.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # H. Zhang and X. Wang, 14 | # "Optimal sensor placement", 15 | # SIAM Review, vol. 35, p. 641, 1993. 16 | 17 | # SIF input: Nick Gould, June 1994 18 | 19 | # classification SUR2-AN-V-0 20 | 21 | param N:=1000; 22 | var theta{i in 1..N} := i/N; 23 | 24 | minimize f: 25 | sum {i in 1..N, j in 1..N} 26 | -(sin(theta[i])*sin(theta[j])*sin(theta[i]-theta[j]))^2; 27 | -------------------------------------------------------------------------------- /cute/sim2bqp.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: another very simple box-constrained quadratic 13 | 14 | # classification QBR2-AN-2-0 15 | 16 | var x1 := 10; 17 | var x2 := 1, >= 0, <= 0.5; 18 | 19 | minimize f: 20 | x2 21 | + (-x1+x2)^2 22 | + (x1+x2)^2 23 | ; 24 | -------------------------------------------------------------------------------- /cute/simbqp.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: a very simple box-constrained quadratic 13 | 14 | # SIF input: Nick Gould, March 1992 15 | 16 | # classification QBR2-AN-2-0 17 | 18 | param xinit{1..2}; 19 | var x{i in 1..2} := xinit[i]; 20 | 21 | minimize f: 22 | x[2]+(-x[1]+x[2])^2+(2*x[1]+x[2])^2; 23 | subject to cons1: 24 | 0.0 <= x[2] <= 0.5; 25 | 26 | data; 27 | param xinit:= 1 10 2 1; 28 | -------------------------------------------------------------------------------- /cute/simpllpa.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # N. Gould, private communication. 14 | 15 | # SIF input: N. Gould, Dec 1989. 16 | 17 | # classification LLR2-AN-2-2 18 | 19 | var x{1..2}>=0; 20 | 21 | minimize f: 22 | 2*x[1]+x[2]; 23 | subject to cons1: 24 | x[1]+x[2]-1.0 >= 0; 25 | subject to cons2: 26 | x[1]+2*x[2]-1.5 >= 0; 27 | -------------------------------------------------------------------------------- /cute/simpllpb.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # N. Gould, private communication. 14 | 15 | # SIF input: Ph. Toint, Dec 1989. 16 | 17 | # classification LLR2-AN-2-3 18 | 19 | var x{1..2} >= 0, := 0.1; 20 | 21 | minimize f: 22 | 1.5*x[1]+x[2]; 23 | subject to cons1: 24 | x[1]+x[2]-1.0 >= 0; 25 | subject to cons2: 26 | x[1]+2*x[2]-1.2 >= 0; 27 | subject to cons3: 28 | 2*x[1]+x[2]-1.2 >= 0; 29 | -------------------------------------------------------------------------------- /cute/sineali.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: on original idea by 13 | # Ali Bouriacha, private communication. 14 | 15 | # SIF input: Nick Gould and Ph. Toint, October, 1993. 16 | 17 | # classification OBR2-AN-V-0 18 | 19 | param N:=20; 20 | param pi := 3.1415926535; 21 | var x{i in 1..N} >= if (i == 1) then -1.5*pi else sqrt(pi)-2*pi, 22 | <= if (i == 1) then 0.5*pi else sqrt(pi), 23 | := 0.0; 24 | 25 | minimize f: 26 | sin(x[1]-1) 27 | + sum {i in 2..N} 100*sin(x[i]-x[i-1]^2) 28 | ; 29 | -------------------------------------------------------------------------------- /cute/sineval.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: problem 4.2 in 13 | # Y. Xiao and F. Zhou, 14 | # "Non-monotone trust region methods with curvilinear path 15 | # in unconstrained optimization", 16 | # Computing, vol. 48, pp. 303-317, 1992. 17 | 18 | # SIF input: F Facchinei, M. Roma and Ph. Toint, June 1994 19 | 20 | # classification SUR2-AN-2-0 21 | 22 | param c:=10D-4; 23 | param xinit{1..2}; 24 | var x{i in 1..2} := xinit[i]; 25 | minimize f: 26 | (x[2]-sin(x[1]))^2/c + x[1]^2/4; 27 | 28 | data; 29 | param xinit:= 1 4.712389 2 -1.0; 30 | -------------------------------------------------------------------------------- /cute/sinquad.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # N. Gould, private communication. 14 | 15 | # SIF input: N. Gould, Dec 1989. 16 | 17 | # classification OUR2-AY-V-0 18 | 19 | param N:=10000; 20 | 21 | var x{1..N} := 0.1; 22 | 23 | minimize f: 24 | (x[1]-1)^4 25 | + sum {i in 2..N-1} (sin(x[i]-x[N])-x[1]^2+x[i]^2)^2 26 | + (x[N]^2-x[1]^2)^2 27 | ; 28 | -------------------------------------------------------------------------------- /cute/sinrosnb.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: a modification of an original idea by 13 | # Ali Bouriacha, private communication. 14 | 15 | # SIF input: Nick Gould and Ph. Toint, October, 1993. 16 | 17 | # classification OQR2-AN-V-V 18 | 19 | param N:=1000; 20 | param pi:=4*atan(1); 21 | 22 | var x{i in 1..N} := if (i==1) then 1 else 1; 23 | 24 | minimize f: 25 | sin(x[1]-1+1.5*pi) 26 | + sum {i in 2..N} 100*sin(-x[i]+1.5*pi+x[i-1]^2) 27 | ; 28 | subject to cons1{i in 2..N}: 29 | 2*pi >= pi-x[i]+x[i-1]^2 >= 0; 30 | subject to cons2: 31 | -pi <= x[1] <= pi; 32 | ; 33 | -------------------------------------------------------------------------------- /cute/sisser.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # F.S. Sisser, 14 | # "Elimination of bounds in optimization problems by transforming 15 | # variables", 16 | # Mathematical Programming 20:110-121, 1981. 17 | 18 | # See also Buckley#216 (p. 91) 19 | 20 | # SIF input: Ph. Toint, Dec 1989. 21 | 22 | # classification OUR2-AN-2-0 23 | 24 | param xinit{1..2}; 25 | var x{i in 1..2} := xinit[i]; 26 | 27 | minimize f: 28 | 3*x[1]^4 - 2*(x[1]*x[2])^2 + 3*x[2]^4; 29 | 30 | data; 31 | param xinit := 1 1.0 2 0.1; 32 | -------------------------------------------------------------------------------- /cute/snake.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # a problem designed by Ph. Toint for experimenting with feasibility 14 | # issues in barrier approaches to nonlinear inequality constraints. 15 | 16 | # SIF input: Ph.L. Toint, September 93. 17 | 18 | # classification LOR2-AN-2-2 19 | 20 | param tip := 0.0001; 21 | var x:=1.0; 22 | var y:=5.0; 23 | minimize f: 24 | x; 25 | subject to cons1: 26 | -y+sin(x) <= 0; 27 | subject to cons2: 28 | -y+tip*x+sin(x) >= 0; 29 | -------------------------------------------------------------------------------- /cute/sosqp1.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification QLR2-AN-V-V 13 | 14 | param N:=10000; 15 | var x{1..N} <= 1, >= -1; 16 | var y{1..N} <= 1, >= -1; 17 | 18 | minimize f: 19 | sum {i in 1..N} x[i]*y[i]; 20 | subject to cons1{i in 1..N}: 21 | x[i]-y[i] = 1; 22 | subject to cons2: 23 | sum {i in 1..N} (x[i]+y[i]) = N; 24 | -------------------------------------------------------------------------------- /cute/sosqp2.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification QLR2-AN-V-V 13 | 14 | param N:=10000; 15 | var x{1..N} <= 1, >= -1; 16 | var y{1..N} <= 1, >= -1; 17 | 18 | minimize f: 19 | sum {i in 1..N} x[i]*y[i]; 20 | subject to cons1{i in 1..N}: 21 | i*x[i]-y[i] = i; 22 | subject to cons2: 23 | sum {i in 1..N} (x[i]+y[i]) = N/2; 24 | -------------------------------------------------------------------------------- /cute/spiral.mod: -------------------------------------------------------------------------------- 1 | # 2 | #************************** 3 | # SET UP THE INITIAL DATA * 4 | #************************** 5 | # Problem : 6 | # ********* 7 | # A nonlinear minmax problem. 8 | # Source: 9 | # E. Polak, J.E. Higgins and D. Mayne, 10 | # "A barrier function for minmax problems", 11 | # Mathematical Programming, vol.54(2), pp. 155-176, 1992. 12 | # SIF input: Ph. Toint, April 1992. 13 | # classification LOR2-AN-3-2 14 | # Solution 15 | 16 | var x1 := 1.41831; 17 | var x2 := -4.79462; 18 | var u := 1.0; 19 | 20 | minimize obj: 21 | u; 22 | 23 | subject to c1: 24 | 0 <= -(x1-(sqrt((x1*x1)+(x2*x2)))*cos((sqrt((x1*x1)+(x2*x2))))) * 25 | (x1-(sqrt((x1*x1)+(x2*x2)))*cos((sqrt((x1*x1)+(x2*x2))))) - 0.0050*x1 * x1 - 26 | 0.0050*x2 * x2 + u; 27 | subject to c2: 28 | 0 <= -(x2-(sqrt((x1*x1)+(x2*x2)))*sin((sqrt((x1*x1)+(x2*x2))))) * 29 | (x2-(sqrt((x1*x1)+(x2*x2)))*sin((sqrt((x1*x1)+(x2*x2))))) - 0.0050*x1 * x1 - 30 | 0.0050*x2 * x2 + u; 31 | -------------------------------------------------------------------------------- /cute/srosenbr.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: problem 21 in 13 | # J.J. More', B.S. Garbow and K.E. Hillstrom, 14 | # "Testing Unconstrained Optimization Software", 15 | # ACM Transactions on Mathematical Software, vol. 7(1), pp. 17-41, 1981. 16 | 17 | # SIF input: Ph. Toint, Dec 1989. 18 | 19 | # classification SUR2-AN-V-0 20 | 21 | param N:=10000; 22 | 23 | var x{i in 1..N} := if (i mod 2 == 1) then -1.2 else 1; 24 | 25 | minimize f: 26 | sum {i in 1..N/2} ( 100*(x[2*i]-x[2*i-1]^2)^2 + (x[2*i-1]-1)^2 ); 27 | -------------------------------------------------------------------------------- /cute/stancmin.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # I.M. Stancu-Minasian 14 | # Private communication, 1992. 15 | 16 | # SDIF input: Ph. Toint, October 1992. 17 | 18 | # classification OLI2-AY-3-2 19 | 20 | var x{1..3} := 50.0, >= 0; 21 | 22 | minimize f: 23 | -(6*x[2]+3*x[1]+2*x[3]-11)/(x[1]+4*x[2]+x[3]+1); 24 | subject to cons1: 25 | 3*x[1]+4*x[2]+x[3]-2 <= 0; 26 | subject to cons2: 27 | x[1]+4*x[2]+x[3]-1 <= 0; 28 | -------------------------------------------------------------------------------- /cute/supersim.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # A.R. Conn, N. Gould and Ph.L. Toint, 14 | # "The LANCELOT User's Manual", 15 | # Dept of Maths, FUNDP, 1991. 16 | 17 | # SIF input: Ph. Toint, Jan 1991. 18 | 19 | # classification LLR2-AN-2-2 20 | 21 | var x >= 0; 22 | var y; 23 | minimize f: 24 | x; 25 | subject to cons1: 26 | x+2*y-2 = 0; 27 | subject to cons2: 28 | 2*x+y-2 = 0; 29 | -------------------------------------------------------------------------------- /cute/tame.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # A.R. Conn, N. Gould and Ph.L. Toint, 14 | # "The LANCELOT User's Manual", 15 | # Dept of Maths, FUNDP, 1991. 16 | 17 | # SIF input: Ph. Toint, Jan 1991. 18 | 19 | # classification QLR2-AN-2-1 20 | 21 | var x >= 0; 22 | var y >= 0; 23 | 24 | minimize f: 25 | (x-y)^2; 26 | subject to cons1: 27 | x+y-1 = 0; 28 | -------------------------------------------------------------------------------- /cute/tfi2.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: 13 | # Y. Tanaka, M. Fukushima, T. Ibaraki, 14 | # "A comparative study of several semi-infinite nonlinear programming 15 | # algorithms", 16 | # EJOR, vol. 36, pp. 92-100, 1988. 17 | 18 | # SIF input: Ph. Toint, April 1992. 19 | 20 | # classification LLR2-AN-3-V 21 | 22 | param M := 10000; 23 | param h := 1/M; 24 | var x{1..3}; 25 | 26 | minimize f: 27 | x[1]+0.5*x[2]+x[3]/3; 28 | subject to cons1{i in 0..M}: 29 | -x[1]-i*h*x[2]-(i*h)^2*x[3]+tan(i*h) <= 0; 30 | -------------------------------------------------------------------------------- /cute/try-b.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification QQR2-AN-2-1 13 | 14 | var x >= 0, := 10.0; 15 | var y >= 0, := 10.0; 16 | 17 | minimize f: 18 | (x-1)^2; 19 | subject to cons1: 20 | -1+(x-1)^2+(y-10)^2 = 0; 21 | -------------------------------------------------------------------------------- /cute/vardim.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: problem 25 in 13 | # J.J. More', B.S. Garbow and K.E. Hillstrom, 14 | # "Testing Unconstrained Optimization Software", 15 | # ACM Transactions on Mathematical Software, vol. 7(1), pp. 17-41, 1981. 16 | 17 | # See also Buckley#72 (p.98). 18 | 19 | # SIF input: Ph. Toint, Dec 1989. 20 | 21 | # classification OUR2-AN-V-0 22 | 23 | param N := 100; 24 | var x{i in 1..N} := 1-i/N; 25 | 26 | minimize f: 27 | sum {i in 1..N} (x[i]-1)^2 + (sum {i in 1..N} i*x[i] - N*(N+1)/2)^2 + (sum {i in 1..N} i*x[i] - N*(N+1)/2)^4; 28 | -------------------------------------------------------------------------------- /cute/yao.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # classification QLR2-AN-V-V 13 | 14 | param p := 2000; 15 | param k := 2; 16 | var x{1..p+k}; 17 | minimize f: 18 | sum {i in 1..p+k} 0.5*(x[i]-sin(i/(p+k)))^2; 19 | subject to cons1{i in 1..p}: 20 | x[i]-2*x[i+1]+x[i+2] >= 0; 21 | subject to cons2: 22 | x[1] >= 0.08; 23 | subject to cons3{i in p+1..p+k}: 24 | x[i] = 0.0; 25 | -------------------------------------------------------------------------------- /cute/zangwil2.mod: -------------------------------------------------------------------------------- 1 | # AMPL Model by Hande Y. Benson 2 | # 3 | # Copyright (C) 2001 Princeton University 4 | # All Rights Reserved 5 | # 6 | # Permission to use, copy, modify, and distribute this software and 7 | # its documentation for any purpose and without fee is hereby 8 | # granted, provided that the above copyright notice appear in all 9 | # copies and that the copyright notice and this 10 | # permission notice appear in all supporting documentation. 11 | 12 | # Source: problem 7 (p. 102) in 13 | # A.R. Buckley, 14 | # "Test functions for unconstrained minimization", 15 | # TR 1989CS-3, Mathematics, statistics and computing centre, 16 | # Dalhousie University, Halifax (CDN), 1989. 17 | 18 | # SIF input: Ph. Toint, Dec 1989. 19 | 20 | # classification QUR2-AN-2-0 21 | 22 | param xinit{1..2}; 23 | var x{i in 1..2} := xinit[i]; 24 | 25 | minimize f: 26 | (-56*x[1]-256*x[2]+991+16*x[1]^2+16*x[2]^2-8*x[1]*x[2])/15; 27 | 28 | data; 29 | param xinit:= 1 3.0 2 8.0; 30 | --------------------------------------------------------------------------------