├── newfile10.pdf ├── main.m ├── func.m └── results with matlab.txt /newfile10.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/dawn0123/nonlinear_optimization_sample_with_matlab/HEAD/newfile10.pdf -------------------------------------------------------------------------------- /main.m: -------------------------------------------------------------------------------- 1 | N = 15 2 | K = 15 3 | a = rand(N, 1); 4 | sa = sum(a); 5 | a = a / sa 6 | b = rand(N, K) 7 | beta = 0.5 8 | x0 = ones(N, 1) 9 | f = @(x)func(x, N, K, a, b, beta); 10 | x = fsolve(f, x0) 11 | f(x) -------------------------------------------------------------------------------- /func.m: -------------------------------------------------------------------------------- 1 | function y = func(x, N, K, a, b, beta) 2 | %FUNC Summary of this function goes here 3 | % Detailed explanation goes here 4 | y = zeros(K, 1); 5 | for k = 1:K 6 | s = 0; 7 | for n = 1:N 8 | sn = 0; 9 | for kk = 1:K 10 | sn = sn + b(n, k) * x(k) ^ beta + 1; 11 | end 12 | s = s + a(n) * K / sn; 13 | end 14 | y(k) = (x(k) + 1) * s - 1; 15 | end -------------------------------------------------------------------------------- /results with matlab.txt: -------------------------------------------------------------------------------- 1 | Test case 1: 2 | 3 | N = 4 | 5 | 3 6 | 7 | 8 | K = 9 | 10 | 3 11 | 12 | 13 | a = 14 | 15 | 0.0994 16 | 0.8963 17 | 0.0043 18 | 19 | 20 | b = 21 | 22 | 0.7749 0.0844 0.8001 23 | 0.8173 0.3998 0.4314 24 | 0.8687 0.2599 0.9106 25 | 26 | 27 | beta = 28 | 29 | 0.5000 30 | 31 | 32 | x0 = 33 | 34 | 1 35 | 1 36 | 1 37 | 38 | x = 39 | 40 | 0.6613 41 | 0.1330 42 | 0.2168 43 | 44 | 45 | ans = 46 | 47 | 1.0e-08 * 48 | 49 | -0.0000 50 | 0.0008 51 | 0.1305 52 | 53 | 54 | Test case 2: 55 | 56 | 57 | N = 58 | 59 | 10 60 | 61 | 62 | K = 63 | 64 | 10 65 | 66 | 67 | a = 68 | 69 | 0.1129 70 | 0.0985 71 | 0.1366 72 | 0.1324 73 | 0.1462 74 | 0.0539 75 | 0.1296 76 | 0.1042 77 | 0.0742 78 | 0.0115 79 | 80 | 81 | b = 82 | 83 | 0.7802 0.7343 0.1175 0.8669 0.7719 0.2941 0.9644 0.7978 0.0594 0.7229 84 | 0.3376 0.0513 0.6407 0.0862 0.2057 0.2374 0.4325 0.4876 0.3158 0.5312 85 | 0.6079 0.0729 0.3288 0.3664 0.3883 0.5309 0.6948 0.7690 0.7727 0.1088 86 | 0.7413 0.0885 0.6538 0.3692 0.5518 0.0915 0.7581 0.3960 0.6964 0.6318 87 | 0.1048 0.7984 0.7491 0.6850 0.2290 0.4053 0.4326 0.2729 0.1253 0.1265 88 | 0.1279 0.9430 0.5832 0.5979 0.6419 0.1048 0.6555 0.0372 0.1302 0.1343 89 | 0.5495 0.6837 0.7400 0.7894 0.4845 0.1123 0.1098 0.6733 0.0924 0.0986 90 | 0.4852 0.1321 0.2348 0.3677 0.1518 0.7844 0.9338 0.4296 0.0078 0.1420 91 | 0.8905 0.7227 0.7350 0.2060 0.7819 0.2916 0.1875 0.4517 0.4231 0.1683 92 | 0.7990 0.1104 0.9706 0.0867 0.1006 0.6035 0.2662 0.6099 0.6556 0.1962 93 | 94 | 95 | beta = 96 | 97 | 0.5000 98 | 99 | 100 | x0 = 101 | 102 | 1 103 | 1 104 | 1 105 | 1 106 | 1 107 | 1 108 | 1 109 | 1 110 | 1 111 | 1 112 | 113 | x = 114 | 115 | 0.2455 116 | 0.1562 117 | 0.2614 118 | 0.2212 119 | 0.1786 120 | 0.1013 121 | 0.2900 122 | 0.2419 123 | 0.0852 124 | 0.0814 125 | 126 | 127 | ans = 128 | 129 | 1.0e-06 * 130 | 131 | 0.0023 132 | 0.0966 133 | 0.0011 134 | 0.0046 135 | 0.0179 136 | 0.4027 137 | 0.0005 138 | 0.0017 139 | 0.9491 140 | 0.9650 141 | 142 | 143 | Test case 3: 144 | 145 | 146 | N = 147 | 148 | 15 149 | 150 | 151 | K = 152 | 153 | 15 154 | 155 | 156 | a = 157 | 158 | 0.0512 159 | 0.0800 160 | 0.0441 161 | 0.1027 162 | 0.1044 163 | 0.0914 164 | 0.0411 165 | 0.0481 166 | 0.0261 167 | 0.0829 168 | 0.0933 169 | 0.0966 170 | 0.0590 171 | 0.0633 172 | 0.0157 173 | 174 | 175 | b = 176 | 177 | 0.8997 0.8266 0.4378 0.4001 0.5708 0.8862 0.6954 0.7343 0.0781 0.5201 0.1008 0.5326 0.3604 0.0034 0.2649 178 | 0.4504 0.3900 0.1170 0.8319 0.9969 0.9311 0.7202 0.4303 0.6690 0.8639 0.5078 0.5539 0.1403 0.2207 0.0684 179 | 0.2057 0.4979 0.8147 0.1343 0.5535 0.1908 0.3469 0.6938 0.5002 0.0977 0.5856 0.6801 0.2601 0.0013 0.4363 180 | 0.8997 0.6948 0.3249 0.0605 0.5155 0.2586 0.5170 0.9452 0.2180 0.9081 0.7629 0.3672 0.0868 0.1892 0.1739 181 | 0.7626 0.8344 0.2462 0.0842 0.3307 0.8979 0.5567 0.7842 0.5716 0.1080 0.0830 0.2393 0.4294 0.1425 0.0261 182 | 0.8825 0.6096 0.3427 0.1639 0.4300 0.5934 0.1565 0.7056 0.1222 0.5170 0.6616 0.5789 0.2573 0.2681 0.9547 183 | 0.2850 0.5747 0.3757 0.3242 0.4918 0.5038 0.5621 0.1093 0.6712 0.1432 0.5170 0.8669 0.2976 0.1749 0.4306 184 | 0.6732 0.3260 0.5466 0.3017 0.0710 0.6128 0.6948 0.3899 0.5996 0.5594 0.1710 0.4068 0.4249 0.1386 0.9616 185 | 0.6643 0.4564 0.5619 0.0117 0.8877 0.8194 0.4265 0.5909 0.0560 0.0046 0.9386 0.1126 0.1192 0.5989 0.7624 186 | 0.1228 0.7138 0.3958 0.5399 0.0646 0.5319 0.8363 0.4594 0.0563 0.7667 0.5905 0.4438 0.4951 0.9011 0.0073 187 | 0.4073 0.8844 0.3981 0.0954 0.4362 0.2021 0.7314 0.0503 0.1525 0.8487 0.4406 0.3002 0.7064 0.9394 0.6800 188 | 0.2753 0.7209 0.5154 0.1465 0.8266 0.4539 0.3600 0.2287 0.0196 0.9168 0.9419 0.4014 0.2436 0.2212 0.7060 189 | 0.7167 0.0186 0.6575 0.6311 0.3945 0.4279 0.4542 0.8342 0.4352 0.9870 0.6559 0.8334 0.7851 0.4827 0.6451 190 | 0.2834 0.6748 0.9509 0.8593 0.6135 0.9661 0.3864 0.0156 0.8322 0.5051 0.4519 0.4036 0.0741 0.3760 0.5523 191 | 0.8962 0.4385 0.7223 0.9742 0.8186 0.6201 0.7756 0.8637 0.6174 0.2714 0.8397 0.3902 0.3939 0.5238 0.2181 192 | 193 | 194 | beta = 195 | 196 | 0.5000 197 | 198 | 199 | x0 = 200 | 201 | 1 202 | 1 203 | 1 204 | 1 205 | 1 206 | 1 207 | 1 208 | 1 209 | 1 210 | 1 211 | 1 212 | 1 213 | 1 214 | 1 215 | 1 216 | 217 | Equation solved. 218 | 219 | fsolve completed because the vector of function values is near zero 220 | as measured by the value of the function tolerance, and 221 | the problem appears regular as measured by the gradient. 222 | 223 | 224 | 225 | x = 226 | 227 | 0.2737 228 | 0.3589 229 | 0.1847 230 | 0.0926 231 | 0.2327 232 | 0.3004 233 | 0.2724 234 | 0.2265 235 | 0.1020 236 | 0.3190 237 | 0.2561 238 | 0.2011 239 | 0.1083 240 | 0.1070 241 | 0.1611 242 | 243 | 244 | ans = 245 | 246 | 1.0e-06 * 247 | 248 | 0.0006 249 | 0.0000 250 | 0.0103 251 | 0.6953 252 | 0.0029 253 | 0.0002 254 | 0.0004 255 | 0.0070 256 | 0.5194 257 | 0.0003 258 | 0.0015 259 | 0.0045 260 | 0.2849 261 | 0.3655 262 | 0.0804 263 | 264 | 265 | Test case 4: 266 | 267 | 268 | N = 269 | 270 | 5 271 | 272 | 273 | K = 274 | 275 | 5 276 | 277 | 278 | a = 279 | 280 | 0.0406 281 | 0.1246 282 | 0.3802 283 | 0.0139 284 | 0.4408 285 | 286 | 287 | b = 288 | 289 | 0.7303 0.9631 0.6241 0.0377 0.2619 290 | 0.4886 0.5468 0.6791 0.8852 0.3354 291 | 0.5785 0.5211 0.3955 0.9133 0.6797 292 | 0.2373 0.2316 0.3674 0.7962 0.1366 293 | 0.4588 0.4889 0.9880 0.0987 0.7212 294 | 295 | 296 | beta = 297 | 298 | -0.5000 299 | 300 | 301 | x0 = 302 | 303 | 1 304 | 1 305 | 1 306 | 1 307 | 1 308 | 309 | Equation solved. 310 | 311 | fsolve completed because the vector of function values is near zero 312 | as measured by the value of the function tolerance, and 313 | the problem appears regular as measured by the gradient. 314 | 315 | 316 | 317 | x = 318 | 319 | 0.6396 320 | 0.6450 321 | 0.7529 322 | 0.5222 323 | 0.7196 324 | 325 | 326 | ans = 327 | 328 | 1.0e-11 * 329 | 330 | -0.0251 331 | -0.0167 332 | 0.0001 333 | -0.1377 334 | -0.0001 335 | 336 | 337 | Test case 5: 338 | 339 | 340 | N = 341 | 342 | 10 343 | 344 | 345 | K = 346 | 347 | 10 348 | 349 | 350 | a = 351 | 352 | 0.0185 353 | 0.1132 354 | 0.0856 355 | 0.1349 356 | 0.1238 357 | 0.1565 358 | 0.1543 359 | 0.0579 360 | 0.1210 361 | 0.0343 362 | 363 | 364 | b = 365 | 366 | 0.0305 0.1829 0.0596 0.6596 0.1734 0.2920 0.9516 0.3015 0.0326 0.6448 367 | 0.7441 0.2399 0.6820 0.5186 0.3909 0.4317 0.9203 0.7011 0.5612 0.3763 368 | 0.5000 0.8865 0.0424 0.9730 0.8314 0.0155 0.0527 0.6663 0.8819 0.1909 369 | 0.4799 0.0287 0.0714 0.6490 0.8034 0.9841 0.7379 0.5391 0.6692 0.4283 370 | 0.9047 0.4899 0.5216 0.8003 0.0605 0.1672 0.2691 0.6981 0.1904 0.4820 371 | 0.6099 0.1679 0.0967 0.4538 0.3993 0.1062 0.4228 0.6665 0.3689 0.1206 372 | 0.6177 0.9787 0.8181 0.4324 0.5269 0.3724 0.5479 0.1781 0.4607 0.5895 373 | 0.8594 0.7127 0.8175 0.8253 0.4168 0.1981 0.9427 0.1280 0.9816 0.2262 374 | 0.8055 0.5005 0.7224 0.0835 0.6569 0.4897 0.4177 0.9991 0.1564 0.3846 375 | 0.5767 0.4711 0.1499 0.1332 0.6280 0.3395 0.9831 0.1711 0.8555 0.5830 376 | 377 | 378 | beta = 379 | 380 | -0.7000 381 | 382 | 383 | x0 = 384 | 385 | 1 386 | 1 387 | 1 388 | 1 389 | 1 390 | 1 391 | 1 392 | 1 393 | 1 394 | 1 395 | 396 | Equation solved. 397 | 398 | fsolve completed because the vector of function values is near zero 399 | as measured by the value of the function tolerance, and 400 | the problem appears regular as measured by the gradient. 401 | 402 | 403 | 404 | x = 405 | 406 | 0.7695 407 | 0.5618 408 | 0.5270 409 | 0.6532 410 | 0.6274 411 | 0.4887 412 | 0.6559 413 | 0.6713 414 | 0.6102 415 | 0.5399 416 | 417 | 418 | ans = 419 | 420 | 1.0e-06 * 421 | 422 | -0.0019 423 | -0.1100 424 | -0.1683 425 | -0.0238 426 | -0.0356 427 | -0.2903 428 | -0.0235 429 | -0.0180 430 | -0.0527 431 | -0.1108 432 | 433 | 434 | Test case 6: 435 | 436 | 437 | N = 438 | 439 | 15 440 | 441 | 442 | K = 443 | 444 | 15 445 | 446 | 447 | a = 448 | 449 | 0.0508 450 | 0.0219 451 | 0.0857 452 | 0.0383 453 | 0.0065 454 | 0.1104 455 | 0.0355 456 | 0.0647 457 | 0.1006 458 | 0.0525 459 | 0.1077 460 | 0.0577 461 | 0.0999 462 | 0.1030 463 | 0.0647 464 | 465 | 466 | b = 467 | 468 | 0.0196 0.7904 0.4070 0.8507 0.2278 0.7690 0.0495 0.1239 0.6210 0.1339 0.1771 0.1781 0.1842 0.4561 0.5338 469 | 0.3309 0.9493 0.7487 0.5606 0.4981 0.5814 0.4896 0.4904 0.5737 0.0309 0.6628 0.3596 0.5972 0.1017 0.1092 470 | 0.4243 0.3276 0.8256 0.9296 0.9009 0.9283 0.1925 0.8530 0.0521 0.9391 0.3308 0.0567 0.2999 0.9954 0.8258 471 | 0.2703 0.6713 0.7900 0.6967 0.5747 0.5801 0.1231 0.8739 0.9312 0.3013 0.8985 0.5219 0.1341 0.3321 0.3381 472 | 0.1971 0.4386 0.3185 0.5828 0.8452 0.0170 0.2055 0.2703 0.7287 0.2955 0.1182 0.3358 0.2126 0.2973 0.2940 473 | 0.8217 0.8335 0.5341 0.8154 0.7386 0.1209 0.1465 0.2085 0.7378 0.3329 0.9884 0.1757 0.8949 0.0620 0.7463 474 | 0.4299 0.7689 0.0900 0.8790 0.5860 0.8627 0.1891 0.5650 0.0634 0.4671 0.5400 0.2089 0.0715 0.2982 0.0103 475 | 0.8878 0.1673 0.1117 0.9889 0.2467 0.4843 0.0427 0.6403 0.8604 0.6482 0.7069 0.9052 0.2425 0.0464 0.0484 476 | 0.3912 0.8620 0.1363 0.0005 0.6664 0.8449 0.6352 0.4170 0.9344 0.0252 0.9995 0.6754 0.0538 0.5054 0.6679 477 | 0.7691 0.9899 0.6787 0.8654 0.0835 0.2094 0.2819 0.2060 0.9844 0.8422 0.2878 0.4685 0.4417 0.7614 0.6035 478 | 0.3968 0.5144 0.4952 0.6126 0.6260 0.5523 0.5386 0.9479 0.8589 0.5590 0.4145 0.9121 0.0133 0.6311 0.5261 479 | 0.8085 0.8843 0.1897 0.9900 0.6609 0.6299 0.6952 0.0821 0.7856 0.8541 0.4648 0.1040 0.8972 0.0899 0.7297 480 | 0.7551 0.5880 0.4950 0.5277 0.7298 0.0320 0.4991 0.1057 0.5134 0.3479 0.7640 0.7455 0.1967 0.0809 0.7073 481 | 0.3774 0.1548 0.1476 0.4795 0.8908 0.6147 0.5358 0.1420 0.1776 0.4460 0.8182 0.7363 0.0934 0.7772 0.7814 482 | 0.2160 0.1999 0.0550 0.8013 0.9823 0.3624 0.4452 0.1665 0.3986 0.0542 0.1002 0.5619 0.3074 0.9051 0.2880 483 | 484 | 485 | beta = 486 | 487 | -0.3000 488 | 489 | 490 | x0 = 491 | 492 | 1 493 | 1 494 | 1 495 | 1 496 | 1 497 | 1 498 | 1 499 | 1 500 | 1 501 | 1 502 | 1 503 | 1 504 | 1 505 | 1 506 | 1 507 | 508 | Equation solved. 509 | 510 | fsolve completed because the vector of function values is near zero 511 | as measured by the value of the function tolerance, and 512 | the problem appears regular as measured by the gradient. 513 | 514 | 515 | 516 | x = 517 | 518 | 0.5597 519 | 0.6043 520 | 0.4336 521 | 0.6804 522 | 0.6798 523 | 0.5327 524 | 0.4263 525 | 0.4290 526 | 0.6131 527 | 0.4655 528 | 0.6333 529 | 0.5319 530 | 0.3297 531 | 0.4624 532 | 0.6008 533 | 534 | 535 | ans = 536 | 537 | 1.0e-11 * 538 | 539 | -0.0002 540 | -0.0000 541 | -0.0158 542 | 0.0000 543 | 0.0000 544 | -0.0003 545 | -0.0240 546 | -0.0169 547 | -0.0001 548 | -0.0038 549 | -0.0001 550 | -0.0010 551 | -0.2951 552 | -0.0040 553 | -0.0002 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