├── Beta.mat ├── phi_mpc.mat ├── phi_ref.mat ├── Beta_mpc.mat ├── robust_vehicle_control_10_delay.m ├── robust_vehicle_control_10_delay_bigger_uncertainties.m ├── README.md ├── LICENSE ├── robust_vehicle_control_without_delay.m ├── robust_vehicle_control_3_delay.m └── penm_log.txt /Beta.mat: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/wenjunliu999/Matrix-Inequalities-Based-Robust-Model-Predictive-Control/HEAD/Beta.mat -------------------------------------------------------------------------------- /phi_mpc.mat: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/wenjunliu999/Matrix-Inequalities-Based-Robust-Model-Predictive-Control/HEAD/phi_mpc.mat -------------------------------------------------------------------------------- /phi_ref.mat: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/wenjunliu999/Matrix-Inequalities-Based-Robust-Model-Predictive-Control/HEAD/phi_ref.mat -------------------------------------------------------------------------------- /Beta_mpc.mat: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/wenjunliu999/Matrix-Inequalities-Based-Robust-Model-Predictive-Control/HEAD/Beta_mpc.mat -------------------------------------------------------------------------------- /robust_vehicle_control_10_delay.m: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/wenjunliu999/Matrix-Inequalities-Based-Robust-Model-Predictive-Control/HEAD/robust_vehicle_control_10_delay.m -------------------------------------------------------------------------------- /robust_vehicle_control_10_delay_bigger_uncertainties.m: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/wenjunliu999/Matrix-Inequalities-Based-Robust-Model-Predictive-Control/HEAD/robust_vehicle_control_10_delay_bigger_uncertainties.m -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Matrix-Inequalities-Based-Robust-Model-Predictive-Control-for-Vehicle-Considering-Model-Uncertaintie 2 | source codes for 'Matrix Inequalities Based Robust Model Predictive Control for Vehicle Considering 3 | Model Uncertainties, External Disturbances and Time-varying Delay' 4 | 5 | Paper published in 6 | 7 | Wenjun Liu, Guang Chen and Alois Knoll 8 | Matrix Inequalities Based Robust Model Predictive Control for Vehicle Considering 9 | Model Uncertainties, External Disturbances and Time-varying Delay. 10 | Frontiers in Neurorobotics 11 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | MIT License 2 | 3 | Copyright (c) 2020 Wenjun Liu 4 | 5 | Permission is hereby granted, free of charge, to any person obtaining a copy 6 | of this software and associated documentation files (the "Software"), to deal 7 | in the Software without restriction, including without limitation the rights 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 9 | copies of the Software, and to permit persons to whom the Software is 10 | furnished to do so, subject to the following conditions: 11 | 12 | The above copyright notice and this permission notice shall be included in all 13 | copies or substantial portions of the Software. 14 | 15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE 21 | SOFTWARE. 22 | -------------------------------------------------------------------------------- /robust_vehicle_control_without_delay.m: -------------------------------------------------------------------------------- 1 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 2 | % Author: Wenjun Liu 3 | % Date: 03/12/2020 4 | % 5 | % Matrix Inequalities Based Robust Model Predictive Control for Vehicle Considering 6 | % Model Uncertainties, External Disturbances 7 | % 8 | % Installation package to be installed---yalmip,penlab 9 | 10 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 11 | 12 | clearvars 13 | close all 14 | clc 15 | 16 | %Vehicle Parameters 17 | vx =10; % m/s [Longitudinal Velocity] 18 | cf =3000; % N/rad [Front wheel coefficient] 19 | cr =3000; % N/rad [Rear wheel coefficient] 20 | a1 =1.0; % m [Front to CG distance] 21 | a2 =1.6; % m [Rear to CG distance] 22 | L =2.6; % m [Wheel Base] 23 | Iz =1650; % Kg.m^2 [Moment of Interia] 24 | m =1000; % Kg [Mass] 25 | 26 | umax = 30*pi/180; % maximum steering angle 27 | umin =-30*pi/180; % minimum steering angle 28 | 29 | %Lateral Control Model: time invariant model fixed longitudinal velocity 30 | Ac =[-(cf+cr)/(m*vx),(-a1*cf+a2*cr)/(m*vx*vx)-1;(-a1*cf+a2*cr)/Iz,-(a1*a1*cf+a2*a2*cr)/(Iz*vx)]; 31 | Bc =[cf/(m*vx);a1*cf/Iz]; 32 | Cc =[0,1]; 33 | Dc = 0; 34 | 35 | dt =0.01;% sec 36 | %discretize model 37 | [A,B,C,~]=c2dm(Ac,Bc,Cc,Dc,dt); 38 | 39 | % model data 40 | 41 | E = [0.01;0.1]; 42 | NA = 0.02*A; 43 | NB = 0.02*B; 44 | nx = 2; % Number of states 45 | nu = 1; % Number of inputs 46 | %ndyn = 2; % Number of polytopic systems 47 | 48 | % MPC data 49 | Q = 5*eye(2); 50 | R = 1; 51 | %tao = 1; 52 | N = 499;% iteration times 53 | 54 | u = sdpvar(repmat(nu,1,N),repmat(1,1,N)); 55 | x = sdpvar(repmat(nx,1,N+1),repmat(1,1,N+1)); 56 | x_d = sdpvar(repmat(nx,1,N+1),repmat(1,1,N+1)); 57 | x_r = sdpvar(repmat(nx,1,N+1),repmat(1,1,N+1)); 58 | 59 | %d = binvar(repmat(2,1,N),repmat(1,1,N)); 60 | load('phi_ref.mat'); 61 | load('Beta.mat'); 62 | load('Beta_mpc.mat'); 63 | load('phi_mpc.mat'); 64 | 65 | % Initial state 66 | x{1} = [0; 0]; 67 | x_r{1} = [Beta(1);phi_ref(1)]; 68 | x_d{1} = [Beta(1);phi_ref(1)]; 69 | % y_r{1} = [phi_ref(1)]; 70 | % temp = x_r{1}; 71 | % y_d{1} = [phi_ref(1)]; 72 | 73 | %A = sdpvar(nx,nx); 74 | %B = sdpvar(nx,1); 75 | 76 | % Controller 77 | LMI1 = cell(9,9); 78 | LMI2 = cell(3,3); 79 | LMI3 = cell(13,13); 80 | LMI4 = cell(3,3); 81 | X = sdpvar(2,2); 82 | G = sdpvar(2,2); 83 | %G = sdpvar(repmat(2,2,2),repmat(2,1,2)); 84 | Y = sdpvar(1,2); 85 | %Y = sdpvar(repmat(2,2,2),repmat(1,1,2)); 86 | Z = sdpvar; 87 | M = eye(2); 88 | lambda = sdpvar(1); 89 | xi = sdpvar(1); 90 | eta = sdpvar(1); 91 | eta1 = sdpvar(1); 92 | epsilon = sdpvar(1); 93 | gamma = 0.000001; 94 | tao = [1 0.6 0.2]; 95 | 96 | 97 | LMI1 = [(-1+lambda)*X zeros(2,1) (A*X+B*Y)' (NA*X+NB*Y)' zeros(2,2); 98 | zeros(1,2) -lambda/(gamma^2)*eye(1) E' zeros(1,2) zeros(1,2); 99 | A*X+B*Y E -X zeros(2,2) (eta1*M')'; 100 | NA*X+NB*Y zeros(2,1) zeros(2,2) -eta1*eye(2) zeros(2,2); 101 | zeros(2,2) zeros(2,1) eta1*M' zeros(2,2) -eta1*eye(2)]; 102 | 103 | F =[]; 104 | F = X > 0; 105 | F =[F, 0= 0]+ [LMI3 < 0]; 136 | 137 | for k = 1:N 138 | d = 0.0000001*sin(k); 139 | H = sin(k); 140 | A = A + M*H*NA; 141 | B = B + M*H*NB; 142 | LMI4 = [ones(1) x{k}'; 143 | x{k} X]; 144 | f = f + [LMI4 >= 0]; 145 | f = [f,umin <= u{k} <= umax];%+ [ H'*H<= eye]; 146 | ops = sdpsettings('warning',1,'verbose',1,'solver','sedumi','cachesolvers',1); 147 | obj = xi; 148 | %optimize(F,[],ops); 149 | sol = optimize(f,obj); 150 | if sol.problem == 0 151 | disp('Solver thinks it is feasible'); 152 | end 153 | 154 | %X = cell2mat(X); 155 | X_ = value(X); 156 | Y_ = value(Y); 157 | u{k} = Y_*inv(X_)*x{k}; 158 | x{k+1} = A*x{k}+ B*u{k} + E*d; 159 | %x{k} = x_d{k} - x_r{k}; 160 | x_d{k+1} = [Beta(k); phi_ref(k)]; 161 | x_r{k+1} = x_d{k+1} + x{k+1} 162 | end 163 | 164 | %% 165 | x_ = cell2mat(x_r(1:end)); 166 | u_ = cell2mat(u); 167 | x = cell2mat(x); 168 | x_d = cell2mat(x_d(1:end)); 169 | 170 | figure 171 | plot(x_d(1,:),'linewidth',2); 172 | hold on 173 | plot(x_(1,:),'r--','linewidth',2); 174 | hold on 175 | plot(Beta_mpc(1:100),'k','linewidth',2); 176 | legend( 'Desired','Robust MPC','MPC'); 177 | figure 178 | plot(x_d(2,:),'linewidth',2); 179 | hold on 180 | plot(x_(2,:),'r--','linewidth',2); 181 | hold on 182 | plot(phi_mpc(1:100),'k','linewidth',2); 183 | legend( 'Desired','Robust MPC','MPC'); 184 | 185 | length_evaluate = length(x_d(1,:)); 186 | Err_beta = sqrt(norm(x_(1,1:length_evaluate)-x_d(1,1:length_evaluate))^2 / length_evaluate); 187 | disp(['beta tracking errors = ', num2str(Err_beta)]) 188 | Err_r = sqrt(norm(x_(2,1:length_evaluate)-x_d(2,1:length_evaluate))^2 / length_evaluate); 189 | disp(['beta tracking = ', num2str(Err_r)]) 190 | 191 | -------------------------------------------------------------------------------- /robust_vehicle_control_3_delay.m: -------------------------------------------------------------------------------- 1 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 2 | % Author: Wenjun Liu 3 | % Date: 03/12/2020 4 | % 5 | % Matrix Inequalities Based Robust Model Predictive Control for Vehicle Considering 6 | % Model Uncertainties, External Disturbances and Time-varying Delay (bounded in 3s) 7 | % 8 | % Installation package to be installed---yalmip,penlab 9 | 10 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 11 | clearvars 12 | yalmip('clear'); 13 | close all 14 | clc 15 | 16 | %Vehicle Parameters 17 | vx =10; % m/s [Longitudinal Velocity] 18 | cf =3000; % N/rad [Front wheel coefficient] 19 | cr =3000; % N/rad [Rear wheel coefficient] 20 | a1 =1.0; % m [Front to CG distance] 21 | a2 =1.6; % m [Rear to CG distance] 22 | L =2.6; % m [Wheel Base] 23 | Iz =1650; % Kg.m^2 [Moment of Interia] 24 | m =1000; % Kg [Mass] 25 | 26 | umax = 30*pi/180; % maximum steering angle 27 | umin =-30*pi/180; % minimum steering angle 28 | 29 | %Lateral Control Model: time invariant model fixed longitudinal velocity 30 | Ac =[-(cf+cr)/(m*vx),(-a1*cf+a2*cr)/(m*vx*vx)-1;(-a1*cf+a2*cr)/Iz,-(a1*a1*cf+a2*a2*cr)/(Iz*vx)]; 31 | Bc =[cf/(m*vx);a1*cf/Iz]; 32 | Cc =[0,1]; 33 | Dc = 0; 34 | 35 | dt =0.01;% sec 36 | %discretize model 37 | [A_temp,B,C,~]=c2dm(Ac,Bc,Cc,Dc,dt); 38 | % model data (time delay considered) 39 | 40 | alpha = 0.8; % The limits 1 and 0 correspond to no delay term and to a completed delay term,respectively. 41 | 42 | A = alpha*A_temp; 43 | A_d = (1-alpha)*A_temp; 44 | % model data 45 | 46 | E = [0.01;0.1]; 47 | NA = 0.05*A; 48 | NB = 0.05*B; 49 | NAd = 0.05*A_d; 50 | nx = 2; % Number of states 51 | nu = 1; % Number of inputs 52 | 53 | % MPC data 54 | Q = 5*eye(2); 55 | R = 1; 56 | %tao = 1; 57 | delay_bound = 3; 58 | N = 499+delay_bound;% iteration times 59 | 60 | % PRI parameter 61 | gamma = 0.8; 62 | gamma_d = 1-gamma; 63 | % 64 | d_s = delay_bound-1; 65 | 66 | u = sdpvar(repmat(nu,1,N),repmat(1,1,N)); 67 | x = sdpvar(repmat(nx,1,N+1),repmat(1,1,N+1)); 68 | x_d = sdpvar(repmat(nx,1,N+1),repmat(1,1,N+1)); 69 | x_r = sdpvar(repmat(nx,1,N+1),repmat(1,1,N+1)); 70 | 71 | load('phi_ref.mat'); 72 | load('Beta.mat'); 73 | 74 | 75 | % Initial state 76 | for i = 1:1:delay_bound 77 | x{i} = [0; 0]; 78 | x_d{i} = [Beta(i+500);phi_ref(i+500)]; 79 | x_r{i} = x_d{i} + x{i}; 80 | end 81 | 82 | % Controller 83 | LMI1 = cell(9,9); 84 | LMI2 = cell(3,3); 85 | LMI3 = cell(13,13); 86 | LMI4 = cell(9,9); 87 | 88 | lambda = sdpvar(1); 89 | X = sdpvar(2,2); 90 | X_d = sdpvar(2,2); 91 | Y = sdpvar(1,2); 92 | Z = sdpvar; 93 | M = eye(2); 94 | 95 | xi = sdpvar(1); 96 | eta = sdpvar(1); 97 | eta1 = sdpvar(1); 98 | epsilon = sdpvar(1); 99 | sigma = sdpvar(1); 100 | rou = 0.001; 101 | tao = [1 0.6 0.2]; 102 | 103 | 104 | % RPI 105 | LMI1 = [gamma*(-1+lambda)*X zeros(2,2) zeros(2,1) (A*X+B*Y)' (NA*X+NB*Y)' sigma*M; 106 | zeros(2,2) gamma_d*(-1+lambda)*X zeros(2,1) (A_d*X)' (NAd*X)' zeros(2,2); 107 | zeros(1,2) zeros(1,2) -lambda/(rou^2) E' zeros(1,2) zeros(1,2); 108 | A*X+B*Y A_d*X E -X zeros(2,2) zeros(2,2) 109 | NA*X+NB*Y NAd*X zeros(2,1) zeros(2,2) -sigma*eye(2) zeros(2,2); 110 | sigma*M' zeros(2,2) zeros(2,1) zeros(2,2) zeros(2,2) -sigma*eye(2);]; 111 | 112 | F =[]; 113 | F = X > 0; 114 | F =[F, 0= 0]+ [LMI3 < 0]; 148 | % f = f + [LMI2 >= 0]+ [LMI3 < 0]; %without RPI 149 | 150 | 151 | %data save 152 | u_record = []; 153 | x_r_record = []; 154 | x_d_record = []; 155 | d_record = []; 156 | x_d_record = [x_d_record value(x_d{delay_bound})]; 157 | x_r_record = [x_r_record value(x{delay_bound})+value(x_d{delay_bound})]; 158 | for k = delay_bound+1:N 159 | d = unidrnd(delay_bound); 160 | d_record = [d_record d]; 161 | p = 0.001*sin(k); 162 | H = sin(k); 163 | A = A + M*H*NA; 164 | B = B + M*H*NB; 165 | A_d = A_d + M*H*NAd; 166 | xi_3 = [x{k}',x{k-1}',x{k-2}',x{k-3}']'; 167 | big_gamma = [X zeros(2,2) zeros(2,2) zeros(2,2); 168 | zeros(2,2) X_d/3 zeros(2,2) zeros(2,2); 169 | zeros(2,2) zeros(2,2) X_d/2 zeros(2,2); 170 | zeros(2,2) zeros(2,2) zeros(2,2) X_d]; 171 | % 172 | LMI4 = [ones(1) xi_3'; 173 | xi_3 big_gamma]; 174 | 175 | f = f + [LMI4 >= 0]; 176 | f = [f,umin <= u{k} <= umax]; 177 | ops = sdpsettings('warning',1,'verbose',1,'solver','sedumi','cachesolvers',1); 178 | obj = xi; 179 | 180 | sol = optimize(f,obj); 181 | if sol.problem == 0 182 | disp('Solver thinks it is feasible'); 183 | end 184 | 185 | X_ = value(X); 186 | Y_ = value(Y); 187 | u{k} = Y_*inv(X_)*x{k}; 188 | x{k+1} = A*x{k}+ A_d*x{k-d}+ B*u{k} + E*p; 189 | 190 | x_d{k+1} = [Beta(k+500); phi_ref(k+500)]; 191 | x_r{k+1} = x_d{k+1} + x{k+1}; 192 | 193 | u_record = [u_record value(u{k})]; 194 | x_d_record = [x_d_record value(x_d{k+1})]; 195 | x_r_record = [x_r_record value(x_r{k+1})]; 196 | 197 | end 198 | 199 | %% 200 | 201 | 202 | figure 203 | plot(x_d_record(1,:),'linewidth',3); 204 | hold on 205 | plot(x_r_record(1,:),'r--','linewidth',3); 206 | legend( 'Desired','Robust MPC'); 207 | 208 | figure 209 | plot(x_d_record(2,:),'linewidth',2); 210 | hold on 211 | plot(x_r_record(2,:),'r--','linewidth',2); 212 | legend( 'Desired','Robust MPC'); 213 | 214 | length_evaluate = length(x_d_record(1,:)); 215 | Err_beta = sqrt(norm(x_r_record(1,1:length_evaluate)-x_d_record(1,1:length_evaluate))^2 / length_evaluate); 216 | disp(['beta tracking errors = ', num2str(Err_beta)]) 217 | Err_r = sqrt(norm(x_r_record(2,1:length_evaluate)-x_d_record(2,1:length_evaluate))^2 / length_evaluate); 218 | disp(['r tracking = ', num2str(Err_r)]) 219 | -------------------------------------------------------------------------------- /penm_log.txt: -------------------------------------------------------------------------------- 1 | Problem name: BMI2 from convertor pen2bmi2() 2 | Description: Structure PENM generated by bmi_define() 3 | Start time: 03-Dec-2020 10:50:52 4 | All option settings (* = set by user): 5 | outlev : 2 6 | outlev_file : 5 7 | out_filename : penm_log.txt 8 | user_prn : [not used] 9 | maxotiter : 100 10 | maxiniter : 100 11 | penalty_update : 0.5 12 | penalty_update_bar : 0.3 13 | mpenalty_update : 0.5 14 | mpenalty_min : 1e-06 15 | mpenalty_border : 1e-06 16 | max_outer_iter : 100 17 | outer_stop_limit : 1e-06 18 | kkt_stop_limit : 0.0001 19 | mlt_update : 0.3 20 | mmlt_update : 0.1 21 | uinit : 1 22 | uinit_box : 1 23 | uinit_eq : 0 24 | umin : 1e-10 25 | pinit : 1 26 | pinit_bar : 1 27 | usebarrier : 0 28 | xinit_mod : 0 29 | max_inner_iter : 100 30 | inner_stop_limit : 0.01 31 | unc_dir_stop_limit : 0.01 32 | unc_solver : 0 33 | unc_linesearch : 3 34 | eq_dir_stop_limit : 0.01 35 | eq_solver : 0 36 | eq_linesearch : 3 37 | eq_solver_warn_max : 4 38 | ls_short_max : 3 39 | min_recover_strategy : 0 40 | min_recover_max : 3 41 | phi_R : -0.5 42 | max_ls_iter : 20 43 | max_lseq_iter : 20 44 | armijo_eps : 0.01 45 | ldl_pivot : 1e-05 46 | pert_update : 2 47 | pert_min : 1e-06 48 | pert_try_max : 50 49 | pert_faster : 1 50 | chol_ordering : 1 51 | luk3_diag : 1 52 | 53 | ******************************************************************************* 54 | PenLab 1.04 (20140125) 55 | ******************************************************************************* 56 | Number of variables 8 57 | Number of matrix variables 0 58 | - degrees of freedom (var. elements) 0 59 | (Function) constraints 60 | - box inequalities 0 61 | - linear inequalities 3 62 | - nonlinear inequalities 0 63 | - linear equalities 0 64 | - nonlinear equalities 0 65 | Matrix constraints 66 | - box inequalities 0 67 | - linear inequalities 1 68 | - nonlinear inequalities 1 69 | 70 | Min./Max. ineq-mult.: 1.000000 / 1.000000 71 | ******************** Start ********************* 72 | Objective 0.0000000000000000E+00 73 | Augmented Lagrangian -7.5515157302456526E-01 74 | |f(x) - Lagr(x)| 7.5515157302456526E-01 75 | Grad augm. lagr. 1.0650892824790795E+12 76 | Feasibility (max) 1.0049881041049954E-01 77 | Feasibility eqx 78 | Feasibility ineq 0.0000000000000000E+00 79 | Feasibility box 80 | Feasibility m.ineq 1.0049881041049954E-01 81 | Complementarity 1.0000000000000000E+00 82 | Minimal penalty 6.9444444444444453E-01 83 | ************************************************ 84 | 85 | ************* Start of outer step 1 ********** 86 | object(x_ 0) = -7.5515157302456526E-01 87 | ||grad(x)||_2 = 1.0650892824790795E+12 88 | --- start of inner iter --- 89 | 90 | Computing ordering 91 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=18 (dim 8x8) 92 | LS (pen): -3.2311e+00, 1 steps, Step width: 1.000000 93 | 94 | object(x_ 1) = -2.8844960213542667E+00 95 | ||grad(x)||_2 = 4.7737494347238959E+11 96 | --- end of 1 in. iter --- 97 | 98 | Reusing ordering 99 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 100 | LS (pen): -2.1657e+00, 1 steps, Step width: 1.000000 101 | 102 | object(x_ 2) = -4.3269604259590855E+00 103 | ||grad(x)||_2 = 2.1285190804610040E+11 104 | --- end of 2 in. iter --- 105 | 106 | Reusing ordering 107 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 108 | LS (pen): -1.4325e+00, 1 steps, Step width: 1.000000 109 | 110 | object(x_ 3) = -5.2760223944319380E+00 111 | ||grad(x)||_2 = 9.4749811943109512E+10 112 | --- end of 3 in. iter --- 113 | 114 | Reusing ordering 115 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 116 | LS (pen): -9.6751e-01, 1 steps, Step width: 1.000000 117 | 118 | object(x_ 4) = -5.9271811988006746E+00 119 | ||grad(x)||_2 = 4.2146183337190239E+10 120 | --- end of 4 in. iter --- 121 | 122 | Reusing ordering 123 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 124 | LS (pen): -7.3809e-01, 1 steps, Step width: 1.000000 125 | 126 | object(x_ 5) = -6.4276704648866172E+00 127 | ||grad(x)||_2 = 1.8738561114465801E+10 128 | --- end of 5 in. iter --- 129 | 130 | Reusing ordering 131 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 132 | LS (pen): -6.0155e-01, 1 steps, Step width: 1.000000 133 | 134 | object(x_ 6) = -6.8383008282840212E+00 135 | ||grad(x)||_2 = 8.3295422912619715E+09 136 | --- end of 6 in. iter --- 137 | 138 | Reusing ordering 139 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 140 | LS (pen): -5.3045e-01, 1 steps, Step width: 1.000000 141 | 142 | object(x_ 7) = -7.2036707474528159E+00 143 | ||grad(x)||_2 = 3.7022637235787740E+09 144 | --- end of 7 in. iter --- 145 | 146 | Reusing ordering 147 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 148 | LS (pen): -5.1355e-01, 1 steps, Step width: 1.000000 149 | 150 | object(x_ 8) = -7.5574456031018498E+00 151 | ||grad(x)||_2 = 1.6455014706038697E+09 152 | --- end of 8 in. iter --- 153 | 154 | Reusing ordering 155 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 156 | LS (pen): -4.7200e-01, 1 steps, Step width: 1.000000 157 | 158 | object(x_ 9) = -7.8754383228210640E+00 159 | ||grad(x)||_2 = 7.3134683915341735E+08 160 | --- end of 9 in. iter --- 161 | 162 | Reusing ordering 163 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 164 | LS (pen): -3.7014e-01, 1 steps, Step width: 1.000000 165 | 166 | object(x_ 10) = -8.1251795921099657E+00 167 | ||grad(x)||_2 = 3.2504634050766897E+08 168 | --- end of 10 in. iter --- 169 | 170 | Reusing ordering 171 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 172 | LS (pen): -3.0748e-01, 1 steps, Step width: 1.000000 173 | 174 | object(x_ 11) = -8.3357506536944577E+00 175 | ||grad(x)||_2 = 1.4446569249775848E+08 176 | --- end of 11 in. iter --- 177 | 178 | Reusing ordering 179 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 180 | LS (pen): -2.8292e-01, 1 steps, Step width: 1.000000 181 | 182 | object(x_ 12) = -8.5308188231575564E+00 183 | ||grad(x)||_2 = 6.4207084730633758E+07 184 | --- end of 12 in. iter --- 185 | 186 | Reusing ordering 187 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 188 | LS (pen): -2.7132e-01, 1 steps, Step width: 1.000000 189 | 190 | object(x_ 13) = -8.7183043203008452E+00 191 | ||grad(x)||_2 = 2.8536497428992819E+07 192 | --- end of 13 in. iter --- 193 | 194 | Reusing ordering 195 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 196 | LS (pen): -2.6428e-01, 1 steps, Step width: 1.000000 197 | 198 | object(x_ 14) = -8.9011147548949445E+00 199 | ||grad(x)||_2 = 1.2682886005303003E+07 200 | --- end of 14 in. iter --- 201 | 202 | Reusing ordering 203 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 204 | LS (pen): -2.5961e-01, 1 steps, Step width: 1.000000 205 | 206 | object(x_ 15) = -9.0808108950170521E+00 207 | ||grad(x)||_2 = 5.6368332570307134E+06 208 | --- end of 15 in. iter --- 209 | 210 | Reusing ordering 211 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 212 | LS (pen): -2.5646e-01, 1 steps, Step width: 1.000000 213 | 214 | object(x_ 16) = -9.2584034339923686E+00 215 | ||grad(x)||_2 = 2.5052536156575033E+06 216 | --- end of 16 in. iter --- 217 | 218 | Reusing ordering 219 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 220 | LS (pen): -2.5433e-01, 1 steps, Step width: 1.000000 221 | 222 | object(x_ 17) = -9.4345774212281839E+00 223 | ||grad(x)||_2 = 1.1134403089511145E+06 224 | --- end of 17 in. iter --- 225 | 226 | Reusing ordering 227 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 228 | LS (pen): -2.5290e-01, 1 steps, Step width: 1.000000 229 | 230 | object(x_ 18) = -9.6097972846695399E+00 231 | ||grad(x)||_2 = 4.9485659050684673E+05 232 | --- end of 18 in. iter --- 233 | 234 | Reusing ordering 235 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 236 | LS (pen): -2.5194e-01, 1 steps, Step width: 1.000000 237 | 238 | object(x_ 19) = -9.7843766604234421E+00 239 | ||grad(x)||_2 = 2.1993048933634322E+05 240 | --- end of 19 in. iter --- 241 | 242 | Reusing ordering 243 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 244 | LS (pen): -2.5130e-01, 1 steps, Step width: 1.000000 245 | 246 | object(x_ 20) = -9.9585269055426835E+00 247 | ||grad(x)||_2 = 9.7741111423559763E+04 248 | --- end of 20 in. iter --- 249 | 250 | Reusing ordering 251 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 252 | LS (pen): -2.5086e-01, 1 steps, Step width: 1.000000 253 | 254 | object(x_ 21) = -1.0132390087848913E+01 255 | ||grad(x)||_2 = 4.3434722431224443E+04 256 | --- end of 21 in. iter --- 257 | 258 | Reusing ordering 259 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 260 | LS (pen): -2.5058e-01, 1 steps, Step width: 1.000000 261 | 262 | object(x_ 22) = -1.0306061456161599E+01 263 | ||grad(x)||_2 = 1.9298551135912196E+04 264 | --- end of 22 in. iter --- 265 | 266 | Reusing ordering 267 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 268 | LS (pen): -2.5038e-01, 1 steps, Step width: 1.000000 269 | 270 | object(x_ 23) = -1.0479604745440724E+01 271 | ||grad(x)||_2 = 8.5713664685080821E+03 272 | --- end of 23 in. iter --- 273 | 274 | Reusing ordering 275 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 276 | LS (pen): -2.5026e-01, 1 steps, Step width: 1.000000 277 | 278 | object(x_ 24) = -1.0653062545188369E+01 279 | ||grad(x)||_2 = 3.8037339050817532E+03 280 | --- end of 24 in. iter --- 281 | 282 | Reusing ordering 283 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 284 | LS (pen): -2.5017e-01, 1 steps, Step width: 1.000000 285 | 286 | object(x_ 25) = -1.0826463285794814E+01 287 | ||grad(x)||_2 = 1.6847969972379815E+03 288 | --- end of 25 in. iter --- 289 | 290 | Reusing ordering 291 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 292 | LS (pen): -2.5011e-01, 1 steps, Step width: 1.000000 293 | 294 | object(x_ 26) = -1.0999825928114094E+01 295 | ||grad(x)||_2 = 7.4307142169866472E+02 296 | --- end of 26 in. iter --- 297 | 298 | Reusing ordering 299 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 300 | LS (pen): -2.5008e-01, 1 steps, Step width: 1.000000 301 | 302 | object(x_ 27) = -1.1173163103851785E+01 303 | ||grad(x)||_2 = 3.2458073505238434E+02 304 | --- end of 27 in. iter --- 305 | 306 | Reusing ordering 307 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 308 | LS (pen): -2.5005e-01, 1 steps, Step width: 1.000000 309 | 310 | object(x_ 28) = -1.1346483218108043E+01 311 | ||grad(x)||_2 = 1.3870560549748669E+02 312 | --- end of 28 in. iter --- 313 | 314 | Reusing ordering 315 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 316 | LS (pen): -2.5003e-01, 1 steps, Step width: 1.000000 317 | 318 | object(x_ 29) = -1.1519791865078993E+01 319 | ||grad(x)||_2 = 5.6362372216319649E+01 320 | --- end of 29 in. iter --- 321 | 322 | Reusing ordering 323 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 324 | LS (pen): -2.5002e-01, 1 steps, Step width: 1.000000 325 | 326 | object(x_ 30) = -1.1693092811089658E+01 327 | ||grad(x)||_2 = 2.0346290225420123E+01 328 | --- end of 30 in. iter --- 329 | 330 | Reusing ordering 331 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 332 | LS (pen): -2.5001e-01, 1 steps, Step width: 1.000000 333 | 334 | object(x_ 31) = -1.1866388683228175E+01 335 | ||grad(x)||_2 = 5.5050410279788240E+00 336 | --- end of 31 in. iter --- 337 | 338 | Reusing ordering 339 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 340 | LS (pen): -2.5001e-01, 1 steps, Step width: 1.000000 341 | 342 | object(x_ 32) = -1.2039681353350995E+01 343 | ||grad(x)||_2 = 7.2252278639533196E-01 344 | --- end of 32 in. iter --- 345 | 346 | Reusing ordering 347 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 348 | LS (pen): -2.5001e-01, 1 steps, Step width: 1.000000 349 | 350 | object(x_ 33) = -1.2212972056037598E+01 351 | ||grad(x)||_2 = 1.6689647601219677E-02 352 | --- end of 33 in. iter --- 353 | 354 | Reusing ordering 355 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 356 | LS (pen): -2.5000e-01, 1 steps, Step width: 1.000000 357 | 358 | object(x_ 34) = -1.2386261423846859E+01 359 | ||grad(x)||_2 = 4.7009151225887385E-06 360 | --- end of 34 in. iter --- 361 | 362 | Unconstr min OK 363 | ************ Result of outer step 1 ********** 364 | Objective 1.4720508144665458E-07 365 | Augmented Lagrangian -1.2386261423846859E+01 366 | |f(x) - f(x_old)| 1.4720508144665458E-07 367 | |f(x) - Lagr(x)| 1.2386261571051941E+01 368 | Grad augm. lagr. 4.7009151225887385E-06 369 | Feasibility (max) 2.5598973780870432E-01 370 | Feasibility eqx 371 | Feasibility ineq 0.0000000000000000E+00 372 | Feasibility box 373 | Feasibility m.ineq 2.5598973780870432E-01 374 | Complementarity 2.5000000000000000E-01 375 | Minimal penalty 6.9444444444444453E-01 376 | Newton steps 34 377 | Inner steps 34 378 | Linesearch steps 34 379 | Time of the minimization step 0.265625 s 380 | - factorizations in the step 0 s 381 | ************************************************ 382 | 383 | ************* Start of outer step 2 ********** 384 | object(x_ 0) = 7.8937260861931746E-01 385 | ||grad(x)||_2 = 2.9477961464668829E+02 386 | --- start of inner iter --- 387 | 388 | Reusing ordering 389 | Chol fact failed (6), new pert: 1.000000e-06 390 | Chol fact OK in 0.000000s, total 0.000000s, no pert=1, pert=1.0000e-06, nnz=29 (dim 8x8) 391 | LS (pen): -1.5388e+00, 1 steps, Step width: 1.000000 392 | 393 | object(x_ 1) = -2.3482522142830359E-01 394 | ||grad(x)||_2 = 1.0843947738070467E+02 395 | --- end of 1 in. iter --- 396 | 397 | Reusing ordering 398 | Chol fact failed (8), new pert: 1.000000e-06 399 | Chol fact failed (8), new pert: 2.000000e-06 400 | Chol fact failed (8), new pert: 4.000000e-06 401 | Chol fact failed (8), new pert: 8.000000e-06 402 | Chol fact failed (8), new pert: 1.600000e-05 403 | Chol fact failed (8), new pert: 3.200000e-05 404 | Chol fact failed (8), new pert: 6.400000e-05 405 | Chol fact failed (8), new pert: 1.280000e-04 406 | Chol fact failed (8), new pert: 2.560000e-04 407 | Chol fact failed (8), new pert: 5.120000e-04 408 | Chol fact failed (8), new pert: 1.024000e-03 409 | Chol fact failed (8), new pert: 2.048000e-03 410 | Chol fact failed (8), new pert: 4.096000e-03 411 | Chol fact failed (8), new pert: 8.192000e-03 412 | Chol fact failed (8), new pert: 1.638400e-02 413 | Chol fact OK in 0.000000s, total 0.000000s, no pert=15, pert=1.6384e-02, nnz=29 (dim 8x8) 414 | LS (pen): -1.3616e+00, 13 steps, Step width: 0.000244 415 | 416 | object(x_ 2) = -2.3515761026099544E-01 417 | ||grad(x)||_2 = 1.0837192656756216E+02 418 | --- end of 2 in. iter --- 419 | 420 | Reusing ordering 421 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 422 | LS (pen): -1.0433e+00, 1 steps, Step width: 1.000000 423 | 424 | object(x_ 3) = -9.2774410529828144E-01 425 | ||grad(x)||_2 = 3.2026294253098591E+01 426 | --- end of 3 in. iter --- 427 | 428 | Reusing ordering 429 | Chol fact failed (5), new pert: 8.192000e-03 430 | Chol fact failed (8), new pert: 1.638400e-02 431 | Chol fact OK in 0.000000s, total 0.000000s, no pert=2, pert=1.6384e-02, nnz=29 (dim 8x8) 432 | LS (pen): -9.9861e-01, 9 steps, Step width: 0.003906 433 | 434 | object(x_ 4) = -9.3164315727868219E-01 435 | ||grad(x)||_2 = 3.1901192927836384E+01 436 | --- end of 4 in. iter --- 437 | 438 | Reusing ordering 439 | Chol fact failed (5), new pert: 8.192000e-03 440 | Chol fact failed (8), new pert: 1.638400e-02 441 | Chol fact OK in 0.000000s, total 0.000000s, no pert=2, pert=1.6384e-02, nnz=29 (dim 8x8) 442 | LS (pen): -9.8864e-01, 12 steps, Step width: 0.000488 443 | 444 | object(x_ 5) = -9.3212586040733381E-01 445 | ||grad(x)||_2 = 3.1885526123347415E+01 446 | --- end of 5 in. iter --- 447 | 448 | Reusing ordering 449 | Chol fact failed (5), new pert: 8.192000e-03 450 | Chol fact failed (8), new pert: 1.638400e-02 451 | Chol fact OK in 0.000000s, total 0.000000s, no pert=2, pert=1.6384e-02, nnz=29 (dim 8x8) 452 | LS (pen): -9.3906e-01, 14 steps, Step width: 0.000122 453 | 454 | object(x_ 6) = -9.3224048876898802E-01 455 | ||grad(x)||_2 = 3.1881328714262988E+01 456 | --- end of 6 in. iter --- 457 | 458 | Reusing ordering 459 | Chol fact failed (5), new pert: 8.192000e-03 460 | Chol fact OK in 0.000000s, total 0.000000s, no pert=1, pert=8.1920e-03, nnz=29 (dim 8x8) 461 | LS (pen): -1.2007e+00, 15 steps, Step width: 0.000061 462 | 463 | object(x_ 7) = -9.3231375421957829E-01 464 | ||grad(x)||_2 = 3.1797696528143803E+01 465 | --- end of 7 in. iter --- 466 | 467 | Reusing ordering 468 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 469 | LS (pen): -6.0787e-01, 1 steps, Step width: 1.000000 470 | 471 | object(x_ 8) = -1.3118703565706138E+00 472 | ||grad(x)||_2 = 5.5374362417968737E+00 473 | --- end of 8 in. iter --- 474 | 475 | Reusing ordering 476 | Chol fact failed (5), new pert: 4.096000e-03 477 | Chol fact failed (5), new pert: 8.192000e-03 478 | Chol fact failed (5), new pert: 1.638400e-02 479 | Chol fact failed (8), new pert: 3.276800e-02 480 | Chol fact OK in 0.000000s, total 0.000000s, no pert=4, pert=3.2768e-02, nnz=29 (dim 8x8) 481 | LS (pen): -1.1175e+00, 14 steps, Step width: 0.000122 482 | 483 | object(x_ 9) = -1.3120067775968107E+00 484 | ||grad(x)||_2 = 5.5366434734445917E+00 485 | --- end of 9 in. iter --- 486 | 487 | Reusing ordering 488 | Chol fact failed (5), new pert: 1.638400e-02 489 | Chol fact OK in 0.000000s, total 0.000000s, no pert=1, pert=1.6384e-02, nnz=29 (dim 8x8) 490 | LS (pen): -1.4991e+00, 17 steps, Step width: 0.000015 491 | 492 | object(x_ 10) = -1.3120296529779454E+00 493 | ||grad(x)||_2 = 5.5361952727126225E+00 494 | --- end of 10 in. iter --- 495 | 496 | Reusing ordering 497 | Chol fact failed (5), new pert: 8.192000e-03 498 | Chol fact OK in 0.000000s, total 0.000000s, no pert=1, pert=8.1920e-03, nnz=29 (dim 8x8) 499 | LS (pen): -1.1603e-01, 14 steps, Step width: 0.000122 500 | 501 | object(x_ 11) = -1.3120438156733290E+00 502 | ||grad(x)||_2 = 5.5339144147610044E+00 503 | --- end of 11 in. iter --- 504 | 505 | Reusing ordering 506 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 507 | LS (pen): -1.1239e-01, 7 steps, Step width: 0.015625 508 | 509 | object(x_ 12) = -1.3137860745038779E+00 510 | ||grad(x)||_2 = 4.6602310446000121E+00 511 | --- end of 12 in. iter --- 512 | 513 | Reusing ordering 514 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 515 | LS (pen): -1.0960e-01, 1 steps, Step width: 1.000000 516 | 517 | object(x_ 13) = -1.3661493141941721E+00 518 | ||grad(x)||_2 = 9.2010401319528345E-01 519 | --- end of 13 in. iter --- 520 | 521 | Reusing ordering 522 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 523 | LS (pen): -4.4636e-02, 2 steps, Step width: 0.500000 524 | 525 | object(x_ 14) = -1.3840961391282702E+00 526 | ||grad(x)||_2 = 9.0133637489664711E+00 527 | --- end of 14 in. iter --- 528 | 529 | Reusing ordering 530 | Chol fact failed (6), new pert: 4.096000e-03 531 | Chol fact OK in 0.000000s, total 0.000000s, no pert=1, pert=4.0960e-03, nnz=29 (dim 8x8) 532 | LS (pen): -1.6483e-03, 1 steps, Step width: 1.000000 533 | 534 | object(x_ 15) = -1.3851656322744490E+00 535 | ||grad(x)||_2 = 3.4196463084015276E+00 536 | --- end of 15 in. iter --- 537 | 538 | Reusing ordering 539 | Chol fact failed (6), new pert: 2.048000e-03 540 | Chol fact OK in 0.000000s, total 0.000000s, no pert=1, pert=2.0480e-03, nnz=29 (dim 8x8) 541 | LS (pen): -4.7394e-04, 1 steps, Step width: 1.000000 542 | 543 | object(x_ 16) = -1.3855228393074139E+00 544 | ||grad(x)||_2 = 1.0169038731987601E+00 545 | --- end of 16 in. iter --- 546 | 547 | Reusing ordering 548 | Chol fact failed (6), new pert: 1.024000e-03 549 | Chol fact OK in 0.000000s, total 0.000000s, no pert=1, pert=1.0240e-03, nnz=29 (dim 8x8) 550 | LS (pen): -2.0255e-04, 1 steps, Step width: 1.000000 551 | 552 | object(x_ 17) = -1.3856677513461095E+00 553 | ||grad(x)||_2 = 1.5402304936711150E-01 554 | --- end of 17 in. iter --- 555 | 556 | Reusing ordering 557 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 558 | LS (pen): -3.7577e-02, 1 steps, Step width: 1.000000 559 | 560 | object(x_ 18) = -1.4116998221853072E+00 561 | ||grad(x)||_2 = 1.3933411904704682E-03 562 | --- end of 18 in. iter --- 563 | 564 | Unconstr min OK 565 | ************ Result of outer step 2 ********** 566 | Objective 7.0834026158144889E-08 567 | Augmented Lagrangian -1.4116998221853072E+00 568 | |f(x) - f(x_old)| 7.6371055288509696E-08 569 | |f(x) - Lagr(x)| 1.4116998930193334E+00 570 | Grad augm. lagr. 1.3933411904704682E-03 571 | Feasibility (max) 2.1462100744247425E-02 572 | Feasibility eqx 573 | Feasibility ineq 0.0000000000000000E+00 574 | Feasibility box 575 | Feasibility m.ineq 2.1462100744247425E-02 576 | Complementarity 3.7499999999999999E-02 577 | Minimal penalty 3.4722222222222227E-01 578 | Newton steps 18 579 | Inner steps 50 580 | Linesearch steps 125 581 | Time of the minimization step 0.390625 s 582 | - factorizations in the step 0 s 583 | ************************************************ 584 | 585 | ************* Start of outer step 3 ********** 586 | object(x_ 0) = -1.6672095262663375E-01 587 | ||grad(x)||_2 = 2.9579828502850480E+00 588 | --- start of inner iter --- 589 | 590 | Reusing ordering 591 | Chol fact OK in 0.062500s, total 0.062500s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 592 | LS (pen): -8.1155e-02, 2 steps, Step width: 0.500000 593 | 594 | object(x_ 1) = -1.9604052380695952E-01 595 | ||grad(x)||_2 = 6.3284652160459776E-01 596 | --- end of 1 in. iter --- 597 | 598 | Reusing ordering 599 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 600 | LS (pen): -1.0898e-02, 5 steps, Step width: 0.062500 601 | 602 | object(x_ 2) = -1.9670067387080969E-01 603 | ||grad(x)||_2 = 5.9148969546613850E-01 604 | --- end of 2 in. iter --- 605 | 606 | Reusing ordering 607 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 608 | LS (pen): -1.0076e-02, 4 steps, Step width: 0.125000 609 | 610 | object(x_ 3) = -1.9788391901504893E-01 611 | ||grad(x)||_2 = 6.3554843382122284E-01 612 | --- end of 3 in. iter --- 613 | 614 | Reusing ordering 615 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 616 | LS (pen): -8.7590e-03, 1 steps, Step width: 1.000000 617 | 618 | object(x_ 4) = -2.0288475991692462E-01 619 | ||grad(x)||_2 = 4.0211589287822264E-01 620 | --- end of 4 in. iter --- 621 | 622 | Reusing ordering 623 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 624 | LS (pen): -5.9897e-03, 1 steps, Step width: 1.000000 625 | 626 | object(x_ 5) = -2.0700098016083476E-01 627 | ||grad(x)||_2 = 1.0500197160102004E-01 628 | --- end of 5 in. iter --- 629 | 630 | Reusing ordering 631 | Chol fact failed (6), new pert: 5.120000e-04 632 | Chol fact OK in 0.000000s, total 0.000000s, no pert=1, pert=5.1200e-04, nnz=29 (dim 8x8) 633 | LS (pen): -5.5734e-05, 1 steps, Step width: 1.000000 634 | 635 | object(x_ 6) = -2.0703226168831831E-01 636 | ||grad(x)||_2 = 7.9119945439224300E-03 637 | --- end of 6 in. iter --- 638 | 639 | Unconstr min OK 640 | ************ Result of outer step 3 ********** 641 | Objective 3.5996593065888199E-08 642 | Augmented Lagrangian -2.0703226168831831E-01 643 | |f(x) - f(x_old)| 3.4837433092256690E-08 644 | |f(x) - Lagr(x)| 2.0703229768491138E-01 645 | Grad augm. lagr. 7.9119945439224300E-03 646 | Feasibility (max) 1.7948865890502928E-03 647 | Feasibility eqx 648 | Feasibility ineq 0.0000000000000000E+00 649 | Feasibility box 650 | Feasibility m.ineq 1.7948865890502928E-03 651 | Complementarity 5.6250000000000007E-03 652 | Minimal penalty 1.7361111111111113E-01 653 | Newton steps 6 654 | Inner steps 7 655 | Linesearch steps 14 656 | Time of the minimization step 0.234375 s 657 | - factorizations in the step 0.0625 s 658 | ************************************************ 659 | 660 | ************* Start of outer step 4 ********** 661 | object(x_ 0) = -3.0375245972476289E-02 662 | ||grad(x)||_2 = 2.3067892599603290E-01 663 | --- start of inner iter --- 664 | 665 | Reusing ordering 666 | Chol fact failed (6), new pert: 2.560000e-04 667 | Chol fact OK in 0.000000s, total 0.000000s, no pert=1, pert=2.5600e-04, nnz=29 (dim 8x8) 668 | LS (pen): -2.5840e-03, 2 steps, Step width: 0.500000 669 | 670 | object(x_ 1) = -3.1212131248327134E-02 671 | ||grad(x)||_2 = 3.7739799227791096E-02 672 | --- end of 1 in. iter --- 673 | 674 | Reusing ordering 675 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 676 | LS (pen): -9.1728e-04, 2 steps, Step width: 0.500000 677 | 678 | object(x_ 2) = -3.1581930076746152E-02 679 | ||grad(x)||_2 = 1.7519929104959778E-01 680 | --- end of 2 in. iter --- 681 | 682 | Reusing ordering 683 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 684 | LS (pen): -8.6395e-04, 1 steps, Step width: 1.000000 685 | 686 | object(x_ 3) = -3.2177120268671769E-02 687 | ||grad(x)||_2 = 6.8967086710361267E-02 688 | --- end of 3 in. iter --- 689 | 690 | Reusing ordering 691 | Chol fact failed (6), new pert: 1.280000e-04 692 | Chol fact OK in 0.000000s, total 0.000000s, no pert=1, pert=1.2800e-04, nnz=29 (dim 8x8) 693 | LS (pen): -1.3152e-07, 1 steps, Step width: 1.000000 694 | 695 | object(x_ 4) = -3.2177187230650085E-02 696 | ||grad(x)||_2 = 2.4773435148062125E-02 697 | --- end of 4 in. iter --- 698 | 699 | Reusing ordering 700 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 701 | LS (pen): -8.4375e-04, 1 steps, Step width: 1.000000 702 | 703 | object(x_ 5) = -3.2762030316359873E-02 704 | ||grad(x)||_2 = 6.9024569031745607E-03 705 | --- end of 5 in. iter --- 706 | 707 | Unconstr min OK 708 | ************ Result of outer step 4 ********** 709 | Objective 3.9415266125864899E-08 710 | Augmented Lagrangian -3.2762030316359873E-02 711 | |f(x) - f(x_old)| 3.4186730599766997E-09 712 | |f(x) - Lagr(x)| 3.2762069731626001E-02 713 | Grad augm. lagr. 6.9024569031745607E-03 714 | Feasibility (max) 1.6420440673828123E-04 715 | Feasibility eqx 716 | Feasibility ineq 0.0000000000000000E+00 717 | Feasibility box 718 | Feasibility m.ineq 1.6420440673828123E-04 719 | Complementarity 8.4374999999999999E-04 720 | Minimal penalty 8.6805555555555566E-02 721 | Newton steps 5 722 | Inner steps 7 723 | Linesearch steps 7 724 | Time of the minimization step 0.15625 s 725 | - factorizations in the step 0 s 726 | ************************************************ 727 | 728 | ************* Start of outer step 5 ********** 729 | object(x_ 0) = -5.0142514271167352E-03 730 | ||grad(x)||_2 = 8.8822525599970229E-03 731 | --- start of inner iter --- 732 | 733 | Reusing ordering 734 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 735 | LS (pen): -2.4001e-04, 2 steps, Step width: 0.500000 736 | 737 | object(x_ 1) = -5.1008846356039375E-03 738 | ||grad(x)||_2 = 1.2419536533630005E-02 739 | --- end of 1 in. iter --- 740 | 741 | Reusing ordering 742 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 743 | LS (pen): -1.2712e-04, 1 steps, Step width: 1.000000 744 | 745 | object(x_ 2) = -5.1888911965785834E-03 746 | ||grad(x)||_2 = 4.7205567437993250E-03 747 | --- end of 2 in. iter --- 748 | 749 | Unconstr min OK 750 | ************ Result of outer step 5 ********** 751 | Objective 8.1955731103084055E-08 752 | Augmented Lagrangian -5.1888911965785834E-03 753 | |f(x) - f(x_old)| 4.2540464977219157E-08 754 | |f(x) - Lagr(x)| 5.1889731523096869E-03 755 | Grad augm. lagr. 4.7205567437993250E-03 756 | Feasibility (max) 9.8203124999999990E-06 757 | Feasibility eqx 758 | Feasibility ineq 0.0000000000000000E+00 759 | Feasibility box 760 | Feasibility m.ineq 9.8203124999999990E-06 761 | Complementarity 1.2656249999999999E-04 762 | Minimal penalty 4.3402777777777783E-02 763 | Newton steps 2 764 | Inner steps 2 765 | Linesearch steps 3 766 | Time of the minimization step 0.0625 s 767 | - factorizations in the step 0 s 768 | ************************************************ 769 | 770 | ************* Start of outer step 6 ********** 771 | object(x_ 0) = -8.0246501290720832E-04 772 | ||grad(x)||_2 = 4.8797901929576752E-03 773 | --- start of inner iter --- 774 | 775 | Reusing ordering 776 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 777 | LS (pen): -1.9893e-05, 1 steps, Step width: 1.000000 778 | 779 | object(x_ 1) = -8.1602592396601617E-04 780 | ||grad(x)||_2 = 2.8568084175477930E-03 781 | --- end of 1 in. iter --- 782 | 783 | Unconstr min OK 784 | ************ Result of outer step 6 ********** 785 | Objective 1.2363146067248530E-07 786 | Augmented Lagrangian -8.1602592396601617E-04 787 | |f(x) - f(x_old)| 4.1675729569401241E-08 788 | |f(x) - Lagr(x)| 8.1614955542668865E-04 789 | Grad augm. lagr. 2.8568084175477930E-03 790 | Feasibility (max) 2.9721679687499995E-04 791 | Feasibility eqx 792 | Feasibility ineq 0.0000000000000000E+00 793 | Feasibility box 794 | Feasibility m.ineq 2.9721679687499995E-04 795 | Complementarity 1.8984374999999999E-05 796 | Minimal penalty 2.1701388888888892E-02 797 | Newton steps 1 798 | Inner steps 1 799 | Linesearch steps 1 800 | Time of the minimization step 0.046875 s 801 | - factorizations in the step 0 s 802 | ************************************************ 803 | 804 | ************* Start of outer step 7 ********** 805 | object(x_ 0) = -1.2624395001928861E-04 806 | ||grad(x)||_2 = 2.8787219443353854E-03 807 | --- start of inner iter --- 808 | 809 | Reusing ordering 810 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 811 | LS (pen): -2.8995e-06, 1 steps, Step width: 1.000000 812 | 813 | object(x_ 1) = -1.2824458615278949E-04 814 | ||grad(x)||_2 = 1.1470911357914536E-03 815 | --- end of 1 in. iter --- 816 | 817 | Unconstr min OK 818 | ************ Result of outer step 7 ********** 819 | Objective 1.8302426181501317E-07 820 | Augmented Lagrangian -1.2824458615278949E-04 821 | |f(x) - f(x_old)| 5.9392801142527879E-08 822 | |f(x) - Lagr(x)| 1.2842761041460449E-04 823 | Grad augm. lagr. 1.1470911357914536E-03 824 | Feasibility (max) 7.2851562499999992E-07 825 | Feasibility eqx 826 | Feasibility ineq 0.0000000000000000E+00 827 | Feasibility box 828 | Feasibility m.ineq 7.2851562499999992E-07 829 | Complementarity 2.8476562499999998E-06 830 | Minimal penalty 1.0850694444444446E-02 831 | Newton steps 1 832 | Inner steps 1 833 | Linesearch steps 1 834 | Time of the minimization step 0.0625 s 835 | - factorizations in the step 0 s 836 | ************************************************ 837 | 838 | ************* Start of outer step 8 ********** 839 | object(x_ 0) = -1.9818095393226615E-05 840 | ||grad(x)||_2 = 1.1337363930195882E-03 841 | --- start of inner iter --- 842 | 843 | Reusing ordering 844 | Chol fact OK in 0.000000s, total 0.000000s, no pert=0, pert=0.0000e+00, nnz=29 (dim 8x8) 845 | LS (pen): -4.3872e-07, 1 steps, Step width: 1.000000 846 | 847 | object(x_ 1) = -2.0119854340682853E-05 848 | ||grad(x)||_2 = 5.1537571382364515E-04 849 | --- end of 1 in. iter --- 850 | 851 | Unconstr min OK 852 | ************ Result of outer step 8 ********** 853 | Objective 2.7013880887229467E-07 854 | Augmented Lagrangian -2.0119854340682853E-05 855 | |f(x) - f(x_old)| 8.7114547057281497E-08 856 | |f(x) - Lagr(x)| 2.0389993149555146E-05 857 | Grad augm. lagr. 5.1537571382364515E-04 858 | Feasibility (max) 6.6250000000000001E-08 859 | Feasibility eqx 860 | Feasibility ineq 0.0000000000000000E+00 861 | Feasibility box 862 | Feasibility m.ineq 6.6250000000000001E-08 863 | Complementarity 4.2714843750000001E-07 864 | Minimal penalty 5.4253472222222229E-03 865 | Newton steps 1 866 | Inner steps 1 867 | Linesearch steps 1 868 | Time of the minimization step 0.046875 s 869 | - factorizations in the step 0 s 870 | ************************************************ 871 | 872 | ************* Start of outer step 9 ********** 873 | object(x_ 0) = -3.1063587668138802E-06 874 | ||grad(x)||_2 = 4.4715076123706861E-04 875 | --- start of inner iter --- 876 | 877 | Reusing ordering 878 | Chol fact failed (6), new pert: 6.400000e-05 879 | Chol fact OK in 0.000000s, total 0.000000s, no pert=1, pert=6.4000e-05, nnz=29 (dim 8x8) 880 | LS (pen): -1.8361e-10, 1 steps, Step width: 1.000000 881 | 882 | object(x_ 1) = -3.1064279886001846E-06 883 | ||grad(x)||_2 = 1.5757133515382097E-04 884 | --- end of 1 in. iter --- 885 | 886 | Unconstr min OK 887 | ************ Result of outer step 9 ********** 888 | Objective 3.7029164096198478E-07 889 | Augmented Lagrangian -3.1064279886001846E-06 890 | |f(x) - f(x_old)| 1.0015283208969010E-07 891 | |f(x) - Lagr(x)| 3.4767196295621695E-06 892 | Grad augm. lagr. 1.5757133515382097E-04 893 | Feasibility (max) 6.6250000000000001E-08 894 | Feasibility eqx 895 | Feasibility ineq 0.0000000000000000E+00 896 | Feasibility box 897 | Feasibility m.ineq 6.6250000000000001E-08 898 | Complementarity 3.7023717253933449E-07 899 | Minimal penalty 2.7126736111111114E-03 900 | Newton steps 1 901 | Inner steps 2 902 | Linesearch steps 1 903 | Time of the minimization step 0.015625 s 904 | - factorizations in the step 0 s 905 | ************************************************ 906 | 907 | ******************************************************************************* 908 | PenLab converged: optimal solution 909 | ******************************************************************************* 910 | Objective 3.7029164096198478E-07 911 | Augmented Lagrangian -3.1064279886001846E-06 912 | Relative precision 3.4767196295621695E-06 913 | Compl. Slackness 3.7023717253933449E-07 914 | Grad augm. lagr. 1.5757133515382097E-04 915 | Feasibility (max) 0.0000000000000000E+00 916 | Feasibility eqx 917 | Feasibility ineq 0.0000000000000000E+00 918 | Feasibility box 919 | Minimal penalty 3.9062500000000000E-03 920 | Newton steps 69 921 | Inner steps 105 922 | Linesearch steps 187 923 | Number of evaluations of 924 | - function values 196 925 | - gradient values 78 926 | - hessian values 69 927 | Time statistics 928 | - total process time 1.46875 s 929 | - all minimization steps 1.28125 s 930 | - all factorizations 0.0625 s 931 | - function values evaluation 0.1875 s 932 | - gradient values evaluation 0.359375 s 933 | - hessian values evaluation 0.4375 s 934 | ******************************************************************************* 935 | 936 | --------------------------------------------------------------------------------