type test10 function S=test(x) % Edgar & Himmelblau, 1988 % x0 = [1, 1]' % xo = [0, 0]' % S(xo) = 0 S=4*x(1).^2-2.*x(1).*x(2)+x(2).^2; type gtest10 function G=test(x) % Gradient of Edgar & Himmelblau, 1988 % x0 = [1, 1]' % xo = [0, 0]' % S(xo) = 0 G(1)=8*x(1)-2*x(2); G(2)=-2*x(1)+2*x(2); [xo,Ot,nS]=steepdes('test10',[1 1],1,'gtest10',0) Pause: hit any key to continue... Directional Iteration Func-count f(x) Step-size derivative 1 0 3 0.166667 -36 Warning: Divide by zero. > In C:\Apps\Matlab\toolbox\optim\cubici2.m at line 12 In C:\Apps\Matlab\toolbox\optim\searchq.m at line 65 In v:\cursos\pos\otimiza\aulas\fminusub.m at line 283 In v:\cursos\pos\otimiza\aulas\fminunc1.m at line 220 In v:\cursos\pos\otimiza\aulas\varmetr.m at line 115 In v:\cursos\pos\otimiza\aulas\steepdes.m at line 51 Warning: Divide by zero. > In C:\Apps\Matlab\toolbox\optim\cubici2.m at line 16 In C:\Apps\Matlab\toolbox\optim\searchq.m at line 65 In v:\cursos\pos\otimiza\aulas\fminusub.m at line 283 In v:\cursos\pos\otimiza\aulas\fminunc1.m at line 220 In v:\cursos\pos\otimiza\aulas\varmetr.m at line 115 In v:\cursos\pos\otimiza\aulas\steepdes.m at line 51 Pause: hit any key to continue... 2 4 0.75 0.125 0 Pause: hit any key to continue... 3 9 0.21 0.6 0.45 Warning: Divide by zero. > In C:\Apps\Matlab\toolbox\optim\cubici2.m at line 12 In C:\Apps\Matlab\toolbox\optim\searchq.m at line 71 In v:\cursos\pos\otimiza\aulas\fminusub.m at line 283 In v:\cursos\pos\otimiza\aulas\fminunc1.m at line 220 In v:\cursos\pos\otimiza\aulas\varmetr.m at line 115 In v:\cursos\pos\otimiza\aulas\steepdes.m at line 51 Warning: Divide by zero. > In C:\Apps\Matlab\toolbox\optim\cubici2.m at line 16 In C:\Apps\Matlab\toolbox\optim\searchq.m at line 71 In v:\cursos\pos\otimiza\aulas\fminusub.m at line 283 In v:\cursos\pos\otimiza\aulas\fminunc1.m at line 220 In v:\cursos\pos\otimiza\aulas\varmetr.m at line 115 In v:\cursos\pos\otimiza\aulas\steepdes.m at line 51 Pause: hit any key to continue... 4 13 0.0138057 0.117834 7.7e-016 Warning: Divide by zero. > In C:\Apps\Matlab\toolbox\optim\cubici2.m at line 12 In C:\Apps\Matlab\toolbox\optim\searchq.m at line 34 In v:\cursos\pos\otimiza\aulas\fminusub.m at line 283 In v:\cursos\pos\otimiza\aulas\fminunc1.m at line 220 In v:\cursos\pos\otimiza\aulas\varmetr.m at line 115 In v:\cursos\pos\otimiza\aulas\steepdes.m at line 51 Warning: Divide by zero. > In C:\Apps\Matlab\toolbox\optim\cubici2.m at line 16 In C:\Apps\Matlab\toolbox\optim\searchq.m at line 34 In v:\cursos\pos\otimiza\aulas\fminusub.m at line 283 In v:\cursos\pos\otimiza\aulas\fminunc1.m at line 220 In v:\cursos\pos\otimiza\aulas\varmetr.m at line 115 In v:\cursos\pos\otimiza\aulas\steepdes.m at line 51 Pause: hit any key to continue... 5 18 0.00142354 0.792857 0.00781 Pause: hit any key to continue... 6 22 0.000107465 0.118106 -8.57e-017 Pause: hit any key to continue... 7 27 1.20867e-005 0.782782 6.09e-005 Optimization terminated successfully: Current search direction is a descent direction, and magnitude of directional derivative in search direction less than 2*options.TolFun Pause: hit any key to continue... xo = 0.0019 0.0006 Ot = 1.2087e-005 nS = 28 help newton Unconstrained optimization using Newton. [xo,Ot,nS]=newton(S,x0,ip,G,H,Lb,Ub,problem,tol,mxit) S: objective function x0: initial point ip: (0) no plot (default), (>0) plot figure ip with pause, (<0) plot figure ip G: gradient vector function H: Hessian matrix function Lb, Ub: lower and upper bound vectors to plot (default = x0*(1+/-2)) problem: (-1): minimum (default), (1): maximum tol: tolerance (default = 1e-4) mxit: maximum number of iterations (default = 50*(1+4*~(ip>0))) xo: optimal point Ot: optimal value of S nS: number of objective function evaluations [xo,Ot,nS]=newton('test10',[1 1],1,'gtest10') Pause: hit any key to continue... Pause: hit any key to continue... xo = 1.0e-031 * 0.1233 0.3287 Ot = 8.7781e-064 nS = 3 help cgrad Unconstrained optimization using conjugate gradients (Fletcher-Reeves). [xo,Ot,nS]=cgrad(S,x0,ip,G,method,Lb,Ub,problem,tol,mxit) S: objective function x0: initial point ip: (0) no plot (default), (>0) plot figure ip with pause, (<0) plot figure ip G: gradient vector function method: line-search method: (0) Coggins (default), (1): Golden Section Lb, Ub: lower and upper bound vectors to plot (default = x0*(1+/-2)) problem: (-1): minimum (default), (1): maximum tol: tolerance (default = 1e-4) mxit: maximum number of iterations (default = 50*(1+4*~(ip>0))) xo: optimal point Ot: optimal value of S nS: number of objective function evaluations [xo,Ot,nS]=cgrad('test10',[1 1],1,'gtest10',0) Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... xo = 1.0e-015 * -0.1698 -0.5848 Ot = 2.5873e-031 nS = 37 [xo,Ot,nS]=steepdes('test1',[-1.2 1],-1,'gtest1',0,[],[],[],[],2000) Directional Iteration Func-count f(x) Step-size derivative 1 0 24.2 0.001 -5.42e+004 2 4 4.12814 0.000786792 -68.5 3 10 2.51901 0.474636 -3.52 4 11 1334.32 1.81761 2.64e+003 5 12 14.6767 0.454632 86.6 6 13 2.39681 0.0873426 1.38 7 18 2.18924 0.00259764 -0.0586 8 23 2.05632 0.0506328 0.025 9 27 1.9435 0.00324456 0.0115 10 32 1.85496 0.0318887 -0.0072 11 36 1.77328 0.0038722 -0.0112 12 41 1.70345 0.0235929 -0.00453 13 45 1.63651 0.00453985 -0.0145 14 50 1.57699 0.018776 -0.00249 15 54 1.51869 0.0052898 -0.0106 16 59 1.46567 0.0155433 -0.00115 17 63 1.41297 0.00616508 -0.0074 18 68 1.36427 0.0131905 -0.000179 19 72 1.3153 0.00722181 -0.0051 20 76 1.26948 0.0113785 -0.000206 21 80 1.22289 0.00855135 0.00296 22 84 1.17882 0.00990883 -0.000124 23 88 1.13349 0.0102947 -0.00223 24 92 1.09014 0.00869839 6.03e-005 25 97 1.04491 0.0127083 -0.00259 26 101 1.00112 0.00765536 -0.001 27 106 0.954494 0.0163651 -0.00364 28 110 0.90861 0.00672118 -0.00179 29 115 0.857986 0.0227281 -0.0158 30 119 0.806848 0.00584408 -0.0038 31 124 0.745361 0.0376699 -0.0624 32 128 0.67918 0.0049208 -0.0142 33 134 0.37907 0.195478 -2.39 34 138 0.30518 0.00280425 -0.989 35 142 0.255314 0.108733 -0.122 36 146 0.237502 0.00248565 -0.000378 37 151 0.223127 0.0560455 -0.000576 38 155 0.211859 0.00238209 -0.000367 39 160 0.202105 0.0455429 -0.000579 40 164 0.193909 0.00230943 -0.000175 41 169 0.186563 0.0391765 -0.000364 42 173 0.180147 0.00225356 -9.63e-005 43 178 0.174274 0.0348427 -0.000233 44 182 0.169019 0.0022082 -5.89e-005 45 187 0.164141 0.0316664 -0.000156 46 191 0.159702 0.00217008 -3.87e-005 47 196 0.155541 0.0292183 -0.000109 48 200 0.151708 0.00213722 -2.69e-005 49 205 0.148087 0.0272614 -7.96e-005 50 209 0.144721 0.00210838 -1.95e-005 51 214 0.141522 0.0256536 -5.97e-005 52 218 0.138528 0.00208269 -1.46e-005 53 223 0.135668 0.0243039 -4.59e-005 54 227 0.132975 0.00205956 -1.12e-005 55 232 0.130394 0.023151 -3.61e-005 56 236 0.127951 0.00203854 -8.8e-006 57 241 0.125603 0.0221522 -2.88e-005 58 245 0.12337 0.00201928 -7.04e-006 59 250 0.121218 0.0212766 -2.34e-005 60 254 0.119166 0.00200151 -5.72e-006 61 259 0.117183 0.0205012 -1.93e-005 62 263 0.115286 0.00198505 -4.71e-006 63 268 0.113449 0.0198085 -1.6e-005 64 272 0.111687 0.0019697 -3.93e-006 65 277 0.109978 0.0191852 -1.35e-005 66 281 0.108336 0.00195534 -3.31e-006 67 286 0.10674 0.0186205 -1.15e-005 68 290 0.105203 0.00194185 -2.81e-006 69 295 0.103707 0.018106 -9.8e-006 70 299 0.102264 0.00192914 -2.41e-006 71 304 0.100858 0.0176348 -8.45e-006 72 308 0.0994988 0.00191713 -2.08e-006 73 313 0.0981734 0.0172012 -7.33e-006 74 317 0.0968906 0.00190574 -1.81e-006 75 322 0.095638 0.0168006 -6.4e-006 76 326 0.094424 0.00189493 -1.58e-006 77 331 0.0932376 0.0164291 -5.62e-006 78 335 0.0920864 0.00188463 -1.39e-006 79 340 0.0909603 0.0160833 -4.96e-006 80 344 0.0898663 0.0018748 -1.23e-006 81 349 0.0887954 0.0157606 -4.4e-006 82 353 0.087754 0.00186541 -1.09e-006 83 358 0.0867338 0.0154584 -3.91e-006 84 362 0.0857407 0.00185641 -9.72e-007 85 367 0.0847672 0.0151748 -3.5e-006 86 371 0.0838187 0.00184779 -8.7e-007 87 376 0.0828883 0.014908 -3.14e-006 88 380 0.0819812 0.0018395 -7.81e-007 89 385 0.0810908 0.0146563 -2.82e-006 90 389 0.080222 0.00183154 -7.04e-007 91 394 0.0793688 0.0144185 -2.55e-006 92 398 0.0785356 0.00182387 -6.37e-007 93 403 0.077717 0.0141932 -2.31e-006 94 407 0.0769171 0.00181647 -5.77e-007 95 412 0.0761309 0.0139796 -2.1e-006 96 416 0.075362 0.00180933 -5.25e-007 97 421 0.074606 0.0137766 -1.91e-006 98 425 0.0738663 0.00180244 -4.79e-007 99 430 0.0731385 0.0135834 -1.74e-006 100 434 0.0724261 0.00179577 -4.38e-007 101 439 0.071725 0.0133993 -1.6e-006 102 443 0.0710382 0.00178931 -4.01e-007 103 448 0.0703621 0.0132235 -1.46e-006 104 452 0.0696995 0.00178306 -3.68e-007 105 457 0.0690469 0.0130555 -1.34e-006 106 461 0.0684071 0.001777 -3.39e-007 107 466 0.0677768 0.0128947 -1.24e-006 108 470 0.0671585 0.00177111 -3.12e-007 109 475 0.0665492 0.0127407 -1.14e-006 110 479 0.0659512 0.0017654 -2.88e-007 111 484 0.0653618 0.0125929 -1.06e-006 112 488 0.0647831 0.00175985 -2.67e-007 113 493 0.0642125 0.012451 -9.77e-007 114 497 0.0636521 0.00175445 -2.47e-007 115 502 0.0630994 0.0123147 -9.06e-007 116 506 0.0625564 0.00174919 -2.29e-007 117 511 0.0620206 0.0121835 -8.41e-007 118 515 0.0614941 0.00174408 -2.13e-007 119 520 0.0609744 0.0120571 -7.82e-007 120 524 0.0604636 0.0017391 -1.99e-007 121 529 0.0599593 0.0119354 -7.28e-007 122 533 0.0594634 0.00173424 -1.85e-007 123 538 0.0589738 0.0118179 -6.79e-007 124 542 0.0584922 0.0017295 -1.73e-007 125 547 0.0580165 0.0117045 -6.34e-007 126 551 0.0575485 0.00172488 -1.61e-007 127 556 0.0570862 0.0115949 -5.93e-007 128 560 0.0566311 0.00172037 -1.51e-007 129 565 0.0561815 0.011489 -5.55e-007 130 569 0.0557389 0.00171596 -1.42e-007 131 574 0.0553015 0.0113865 -5.2e-007 132 578 0.0548708 0.00171166 -1.33e-007 133 583 0.0544451 0.0112873 -4.88e-007 134 587 0.0540257 0.00170745 -1.25e-007 135 592 0.0536112 0.0111912 -4.58e-007 136 596 0.0532028 0.00170333 -1.17e-007 137 601 0.052799 0.011098 -4.31e-007 138 605 0.052401 0.00169931 -1.1e-007 139 610 0.0520075 0.0110076 -4.05e-007 140 614 0.0516196 0.00169537 -1.04e-007 141 619 0.0512359 0.0109199 -3.82e-007 142 623 0.0508577 0.00169151 -9.8e-008 143 628 0.0504835 0.0108347 -3.6e-007 144 632 0.0501145 0.00168774 -9.25e-008 145 637 0.0497495 0.0107519 -3.4e-007 146 641 0.0493894 0.00168404 -8.73e-008 147 646 0.0490332 0.0106715 -3.21e-007 148 650 0.0486817 0.00168041 -8.25e-008 149 655 0.0483339 0.0105932 -3.03e-007 150 659 0.0479907 0.00167685 -7.81e-008 151 664 0.0476511 0.0105171 -2.87e-007 152 668 0.0473158 0.00167337 -7.39e-008 153 673 0.046984 0.010443 -2.71e-007 154 677 0.0466565 0.00166995 -7.01e-008 155 682 0.0463322 0.0103708 -2.57e-007 156 686 0.0460121 0.00166659 -6.64e-008 157 691 0.0456952 0.0103005 -2.44e-007 158 695 0.0453822 0.0016633 -6.3e-008 159 700 0.0450723 0.010232 -2.31e-007 160 704 0.0447663 0.00166007 -5.98e-008 161 709 0.0444632 0.0101651 -2.19e-007 162 713 0.0441638 0.00165689 -5.69e-008 163 718 0.0438673 0.0100999 -2.08e-007 164 722 0.0435744 0.00165377 -5.41e-008 165 727 0.0432842 0.0100363 -1.98e-007 166 731 0.0429975 0.00165071 -5.14e-008 167 736 0.0427135 0.00997422 -1.88e-007 168 740 0.0424329 0.0016477 -4.9e-008 169 745 0.0421548 0.00991357 -1.79e-007 170 749 0.0418801 0.00164474 -4.66e-008 171 754 0.0416078 0.00985432 -1.71e-007 172 758 0.0413386 0.00164183 -4.44e-008 173 763 0.0410719 0.00979642 -1.63e-007 174 767 0.0408083 0.00163897 -4.24e-008 175 772 0.040547 0.00973983 -1.55e-007 176 776 0.0402887 0.00163616 -4.04e-008 177 781 0.0400326 0.00968449 -1.48e-007 178 785 0.0397795 0.00163339 -3.86e-008 179 790 0.0395285 0.00963035 -1.41e-007 180 794 0.0392803 0.00163066 -3.69e-008 181 799 0.0390343 0.00957739 -1.35e-007 182 803 0.0387909 0.00162798 -3.52e-008 183 808 0.0385497 0.00952555 -1.29e-007 184 812 0.0383111 0.00162534 -3.37e-008 185 817 0.0380745 0.0094748 -1.23e-007 186 821 0.0378404 0.00162275 -3.22e-008 187 826 0.0376083 0.00942511 -1.18e-007 188 830 0.0373787 0.00162019 -3.08e-008 189 835 0.037151 0.00937643 -1.13e-007 190 839 0.0369257 0.00161767 -2.95e-008 191 844 0.0367023 0.00932873 -1.08e-007 192 848 0.0364811 0.00161518 -2.83e-008 193 853 0.0362618 0.00928199 -1.03e-007 194 857 0.0360448 0.00161274 -2.71e-008 195 862 0.0358295 0.00923617 -9.89e-008 196 866 0.0356165 0.00161033 -2.6e-008 197 871 0.0354051 0.00919125 -9.48e-008 198 875 0.0351959 0.00160795 -2.49e-008 199 880 0.0349883 0.00914719 -9.09e-008 200 884 0.0347828 0.00160561 -2.39e-008 201 889 0.034579 0.00910397 -8.72e-008 202 893 0.0343772 0.0016033 -2.29e-008 203 898 0.034177 0.00906156 -8.36e-008 204 902 0.0339787 0.00160103 -2.2e-008 205 907 0.033782 0.00901994 -8.03e-008 206 911 0.0335872 0.00159878 -2.12e-008 207 916 0.0333939 0.00897909 -7.71e-008 208 920 0.0332025 0.00159657 -2.03e-008 209 925 0.0330125 0.00893898 -7.4e-008 210 929 0.0328244 0.00159439 -1.96e-008 211 934 0.0326377 0.00889959 -7.11e-008 212 938 0.0324527 0.00159223 -1.88e-008 213 943 0.0322692 0.0088609 -6.84e-008 214 947 0.0320874 0.00159011 -1.81e-008 215 952 0.0319069 0.0088229 -6.58e-008 216 956 0.0317282 0.00158801 -1.74e-008 217 961 0.0315507 0.00878555 -6.33e-008 218 965 0.031375 0.00158594 -1.68e-008 219 970 0.0312005 0.00874885 -6.09e-008 220 974 0.0310276 0.0015839 -1.61e-008 221 979 0.030856 0.00871278 -5.86e-008 222 983 0.0306859 0.00158188 -1.55e-008 223 988 0.0305171 0.00867731 -5.64e-008 224 992 0.0303498 0.00157989 -1.5e-008 225 997 0.0301837 0.00864244 -5.43e-008 226 1001 0.0300191 0.00157792 -1.44e-008 227 1006 0.0298557 0.00860814 -5.23e-008 228 1010 0.0296937 0.00157598 -1.39e-008 229 1015 0.0295329 0.00857441 -5.04e-008 230 1019 0.0293735 0.00157406 -1.34e-008 231 1024 0.0292152 0.00854122 -4.86e-008 232 1028 0.0290583 0.00157217 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0.00023449 0.00129586 -1e-013 1787 8026 0.0002339 0.00485269 -3.13e-013 1788 8030 0.000233312 0.0012958 -9.74e-014 1789 8035 0.000232725 0.0048521 -3.09e-013 1790 8039 0.00023214 0.00129574 -9.61e-014 1791 8044 0.000231556 0.00485151 -3.07e-013 1792 8048 0.000230974 0.00129568 -9.78e-014 1793 8053 0.000230393 0.00485092 -3.04e-013 1794 8057 0.000229814 0.00129562 -9.28e-014 1795 8062 0.000229236 0.00485033 -3.01e-013 1796 8066 0.00022866 0.00129556 -9.38e-014 1797 8071 0.000228085 0.00484975 -2.97e-013 1798 8075 0.000227512 0.0012955 -9.35e-014 1799 8080 0.00022694 0.00484916 -2.94e-013 1800 8084 0.00022637 0.00129544 -9.22e-014 1801 8089 0.000225801 0.00484858 -2.91e-013 1802 8093 0.000225234 0.00129539 -9.25e-014 1803 8098 0.000224668 0.004848 -2.87e-013 1804 8102 0.000224104 0.00129533 -8.73e-014 1805 8107 0.000223541 0.00484742 -2.85e-013 1806 8111 0.000222979 0.00129527 -8.8e-014 1807 8116 0.000222419 0.00484684 -2.82e-013 1808 8120 0.000221861 0.00129521 -8.62e-014 1809 8125 0.000221304 0.00484627 -2.79e-013 1810 8129 0.000220748 0.00129516 -8.78e-014 1811 8134 0.000220194 0.00484569 -2.77e-013 1812 8138 0.000219641 0.0012951 -8.62e-014 1813 8143 0.00021909 0.00484512 -2.73e-013 1814 8147 0.00021854 0.00129504 -8.61e-014 1815 8152 0.000217992 0.00484455 -2.7e-013 1816 8156 0.000217444 0.00129498 -7.92e-014 1817 8161 0.000216899 0.00484398 -2.67e-013 1818 8165 0.000216355 0.00129493 -8.38e-014 1819 8170 0.000215812 0.00484341 -2.64e-013 1820 8174 0.00021527 0.00129487 -8.2e-014 1821 8179 0.00021473 0.00484285 -2.61e-013 1822 8183 0.000214192 0.00129481 -8.34e-014 1823 8188 0.000213655 0.00484228 -2.58e-013 1824 8192 0.000213119 0.00129476 -8.08e-014 1825 8197 0.000212584 0.00484172 -2.56e-013 1826 8201 0.000212051 0.0012947 -7.74e-014 1827 8206 0.00021152 0.00484116 -2.54e-013 1828 8210 0.000210989 0.00129464 -7.79e-014 1829 8215 0.00021046 0.0048406 -2.51e-013 1830 8219 0.000209933 0.00129459 -7.83e-014 1831 8224 0.000209407 0.00484004 -2.47e-013 1832 8228 0.000208882 0.00129453 -7.63e-014 1833 8233 0.000208358 0.00483948 -2.45e-013 1834 8237 0.000207836 0.00129448 -7.8e-014 1835 8242 0.000207315 0.00483893 -2.43e-013 1836 8246 0.000206796 0.00129442 -7.51e-014 1837 8251 0.000206278 0.00483838 -2.41e-013 1838 8255 0.000205761 0.00129437 -7.25e-014 1839 8260 0.000205246 0.00483783 -2.39e-013 1840 8264 0.000204732 0.00129431 -7.14e-014 1841 8269 0.000204219 0.00483728 -2.35e-013 1842 8273 0.000203707 0.00129426 -7.56e-014 1843 8278 0.000203197 0.00483673 -2.33e-013 1844 8282 0.000202689 0.0012942 -6.71e-014 1845 8287 0.000202181 0.00483618 -2.31e-013 1846 8291 0.000201675 0.00129415 -7.15e-014 1847 8296 0.00020117 0.00483563 -2.28e-013 1848 8300 0.000200667 0.00129409 -6.92e-014 1849 8305 0.000200164 0.00483509 -2.26e-013 1850 8309 0.000199663 0.00129404 -6.88e-014 1851 8314 0.000199164 0.00483455 -2.23e-013 1852 8318 0.000198665 0.00129398 -6.69e-014 1853 8323 0.000198168 0.00483401 -2.22e-013 1854 8327 0.000197672 0.00129393 -7.01e-014 1855 8332 0.000197178 0.00483347 -2.19e-013 1856 8336 0.000196685 0.00129387 -6.57e-014 1857 8341 0.000196193 0.00483293 -2.17e-013 1858 8345 0.000195702 0.00129382 -6.79e-014 1859 8350 0.000195212 0.00483239 -2.14e-013 1860 8354 0.000194724 0.00129377 -6.49e-014 1861 8359 0.000194237 0.00483186 -2.13e-013 1862 8363 0.000193752 0.00129371 -6.59e-014 1863 8368 0.000193267 0.00483133 -2.09e-013 1864 8372 0.000192784 0.00129366 -6.34e-014 Optimization terminated successfully: Current search direction is a descent direction, and magnitude of directional derivative in search direction less than 2*options.TolFun xo = 0.9861 0.9724 Ot = 1.9247e-004 nS = 8373 [xo,Ot,nS]=newton('test1',[-1.2 1],-1,'gtest1') xo = 1.0000 1.0000 Ot = 4.5475e-024 nS = 35 [xo,Ot,nS]=cgrad('test1',[-1.2 1],1,'gtest1',0) Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... xo = 1.0000 1.0000 Ot = 3.1054e-010 nS = 507 help newton Unconstrained optimization using Newton. [xo,Ot,nS]=newton(S,x0,ip,G,H,Lb,Ub,problem,tol,mxit) S: objective function x0: initial point ip: (0) no plot (default), (>0) plot figure ip with pause, (<0) plot figure ip G: gradient vector function H: Hessian matrix function Lb, Ub: lower and upper bound vectors to plot (default = x0*(1+/-2)) problem: (-1): minimum (default), (1): maximum tol: tolerance (default = 1e-4) mxit: maximum number of iterations (default = 50*(1+4*~(ip>0))) xo: optimal point Ot: optimal value of S nS: number of objective function evaluations type test10 function S=test(x) % Edgar & Himmelblau, 1988 % x0 = [1, 1]' % xo = [0, 0]' % S(xo) = 0 S=4*x(1).^2-2.*x(1).*x(2)+x(2).^2; [xo,Ot,nS]=newton('test10',[1 1],1,'gtest10',[],[-6 -6],[6 6]) Pause: hit any key to continue... Error in ==> v:\cursos\pos\otimiza\aulas\newton.m On line 87 ==> disp('Pause: hit any key to continue...'); pause; type test9 function S=test(x) % Himmelblau, 1972 % x0 = [1, 1]' % xo = [3, 2]', xo = [3.58443, -1.84813]', xo = [-3.7793, -3.2832]' e xo = [-2.8051, 3.1313]' % S(xo) = 0 % local maximum: xo = [-0.2708, -0.9230]', S(xo) = 181.6 S=(x(1).^2+x(2)-11).^2+(x(1)+x(2).^2-7).^2; [xo,Ot,nS]=newton('test9',[1 1],1,'gtest9',[],[-6 -6],[6 6]) Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... xo = 3.3852 0.0739 Ot = 13.3119 nS = 14 edit newton disp(sprintf('%d',feature('SessionTool'))) 0 ; dbstatus dbstack dbstack ; disp(which('newton')); v:\cursos\pos\otimiza\aulas\newton.m mdbstatus 'v:\cursos\pos\otimiza\aulas\newton.m' eval( 'if exist(''stepsize'',''var''), mauifunc(stepsize), end', ''); eval( 'if exist(''y0'',''var''), mauifunc(y0), end', ''); eval( 'if exist(''nS'',''var''), mauifunc(nS), end', ''); 14 eval( 'if exist(''feval'',''var''), mauifunc(feval), end', ''); eval( 'if exist(''xo'',''var''), mauifunc(xo), end', ''); 3.3852 0.0739 eval( 'if exist(''stepsize'',''var''), mauifunc(stepsize), end', ''); eval( 'if exist(''problem'',''var''), mauifunc(problem), end', ''); disp(which('newton_h')); disp(char(which('newton_h','-all'))); eval( 'if exist(''gr'',''var''), mauifunc(gr), end', ''); disp(which('newton_h')); disp(char(which('newton_h','-all'))); [xo,Ot,nS]=newton_h('test9',[1 1],1,'gtest9',[],[-6 -6],[6 6]) ??? Undefined function or variable 'newton_h'. clear function [xo,Ot,nS]=newton_h('test9',[1 1],1,'gtest9',[],[-6 -6],[6 6]) ??? Undefined function or variable 'newton_h'. cd(cd) [xo,Ot,nS]=newton_h('test9',[1 1],1,'gtest9',[],[-6 -6],[6 6]) Pause: hit any key to continue... ans = 29.3137 6.6863 Pause: hit any key to continue... ans = 13.1586 -26.8391 Pause: hit any key to continue... ans = -29.1615 14.7724 Pause: hit any key to continue... ans = -59.7394 11.1417 Pause: hit any key to continue... ans = -112.1471 13.2984 Pause: hit any key to continue... ans = -98.4725 14.0845 Pause: hit any key to continue... ans = -97.5522 14.1349 xo = 3.3852 0.0739 Ot = 13.3119 nS = 14 eval( 'if exist(''S'',''var''), mauifunc(S), end', ''); eval( 'if exist(''stepsize'',''var''), mauifunc(stepsize), end', ''); eval( 'if exist(''he'',''var''), mauifunc(he), end', ''); eval( 'if exist(''gr'',''var''), mauifunc(gr), end', ''); eval( 'if exist(''he'',''var''), mauifunc(he), end', ''); eye(3) ans = 1 0 0 0 1 0 0 0 1 eval( 'if exist(''eye'',''var''), mauifunc(eye), end', ''); eval( 'if exist(''n'',''var''), mauifunc(n), end', ''); eval( 'if exist(''eye'',''var''), mauifunc(eye), end', ''); eval( 'if exist(''he'',''var''), mauifunc(he), end', ''); disp(which('newton_h')); v:\cursos\pos\otimiza\aulas\newton_h.m clear 'v:\cursos\pos\otimiza\aulas\newton_h.m' eval( 'if exist(''stepsize'',''var''), mauifunc(stepsize), end', ''); eval( 'if exist(''x'',''var''), mauifunc(x), end', ''); cd(cd);clear functions [xo,Ot,nS]=newton_h('test9',[1 1],1,'gtest9',[],[-6 -6],[6 6]) Pause: hit any key to continue... ans = 129.3137 106.6863 Pause: hit any key to continue... ans = 124.6055 99.8464 Pause: hit any key to continue... ans = 118.4034 91.3151 Pause: hit any key to continue... ans = 110.4134 80.8896 Pause: hit any key to continue... ans = 100.4796 68.4851 Pause: hit any key to continue... ans = 88.8717 54.3142 Pause: hit any key to continue... ans = 39.3067 76.8920 Pause: hit any key to continue... ans = 26.2187 67.7696 Pause: hit any key to continue... ans = 21.0371 66.0340 Pause: hit any key to continue... ans = 21.8674 68.4425 Pause: hit any key to continue... ans = 19.5076 68.6701 Pause: hit any key to continue... ans = 20.3996 70.3808 Pause: hit any key to continue... ans = 18.5461 70.4641 Pause: hit any key to continue... ans = 19.7750 71.8208 Pause: hit any key to continue... ans = 17.8355 71.5773 Pause: hit any key to continue... ans = 19.6238 72.8582 Pause: hit any key to continue... ans = 17.1806 72.2212 Pause: hit any key to continue... ans = 17.8587 72.5864 Pause: hit any key to continue... ans = 18.8353 73.3083 Pause: hit any key to continue... ans = 17.4137 72.9800 Pause: hit any key to continue... ans = 19.0237 73.8422 Pause: hit any key to continue... ans = 16.8849 73.1499 Pause: hit any key to continue... ans = 17.5517 73.4501 Pause: hit any key to continue... ans = 18.5139 73.9688 Pause: hit any key to continue... ans = 18.1858 73.8656 Pause: hit any key to continue... ans = 17.5636 73.7251 Pause: hit any key to continue... ans = 17.7466 73.8190 Pause: hit any key to continue... ans = 18.0297 74.0141 Pause: hit any key to continue... ans = 17.6020 73.9148 Pause: hit any key to continue... ans = 17.7293 73.9788 Pause: hit any key to continue... ans = 17.9287 74.1109 Pause: hit any key to continue... ans = 17.6289 74.0385 Pause: hit any key to continue... ans = 17.7192 74.0829 Pause: hit any key to continue... ans = 17.8618 74.1737 Pause: hit any key to continue... ans = 17.6490 74.1200 Pause: hit any key to continue... ans = 17.7137 74.1511 Pause: hit any key to continue... ans = 17.8167 74.2141 Pause: hit any key to continue... ans = 17.6644 74.1740 Pause: hit any key to continue... ans = 17.7111 74.1960 Pause: hit any key to continue... ans = 17.7861 74.2400 Pause: hit any key to continue... ans = 17.6763 74.2099 Pause: hit any key to continue... ans = 17.7102 74.2256 Pause: hit any key to continue... ans = 17.7650 74.2566 Pause: hit any key to continue... ans = 17.7451 74.2509 Pause: hit any key to continue... ans = 17.7101 74.2451 Pause: hit any key to continue... ans = 17.7506 74.2672 xo = 2.9995 2.0007 Ot = 9.3290e-006 nS = 115 eval( 'if exist(''problem'',''var''), mauifunc(problem), end', ''); disp(which('newton_h')); v:\cursos\pos\otimiza\aulas\newton_h.m clear 'v:\cursos\pos\otimiza\aulas\newton_h.m' eval( 'if exist(''stepsize'',''var''), mauifunc(stepsize), end', ''); cd(cd);clear functions [xo,Ot,nS]=newton_h('test9',[1 1],1,'gtest9',[],[-6 -6],[6 6]) Pause: hit any key to continue... ans = 59.3137 36.6863 Pause: hit any key to continue... ans = 45.0515 14.2359 Pause: hit any key to continue... ans = -11.4614 -75.9316 Pause: hit any key to continue... ans = -68.8260 -22.8020 Pause: hit any key to continue... ans = -57.0845 11.1544 Pause: hit any key to continue... ans = -56.4380 3.0166 Pause: hit any key to continue... ans = -51.0514 7.0007 Pause: hit any key to continue... ans = -50.3211 6.2765 Pause: hit any key to continue... ans = -50.6708 6.4546 Pause: hit any key to continue... ans = -50.4984 6.3308 Pause: hit any key to continue... ans = -50.5844 6.3829 Pause: hit any key to continue... ans = -50.5414 6.3546 Pause: hit any key to continue... ans = -50.5629 6.3682 xo = 2.9832 1.9507 Ot = 0.0673 nS = 61 eval( 'if exist(''stepsize'',''var''), mauifunc(stepsize), end', ''); eval( 'if exist(''gr'',''var''), mauifunc(gr), end', ''); eval( 'if exist(''end'',''var''), mauifunc(end), end', ''); dbstack ; disp(which('newtont')); v:\cursos\pos\otimiza\aulas\newtont.m mdbstatus 'v:\cursos\pos\otimiza\aulas\newtont.m' eval( 'if exist(''x'',''var''), mauifunc(x), end', ''); eval( 'if exist(''x'',''var''), mauifunc(x), end', ''); ; help newtont Unconstrained optimization using Newton with trust region. [xo,Ot,nS]=newtont(S,x0,G,ip,H,Lb,Ub,problem,tol,mxit) S: objective function x0: initial point G: gradient vector function ip: (0) no plot (default), (>0) plot figure ip with pause, (<0) plot figure ip H: Hessian matrix function (default = sparse finite-differences) Lb, Ub: lower and upper bound vectors to plot (default = x0*(1+/-2)) problem: (-1): minimum (default), (1): maximum tol: tolerance (default = 1e-4) mxit: maximum number of iterations (default = 50*(1+4*~(ip>0))) xo: optimal point Ot: optimal value of S nS: number of objective function evaluations [xo,Ot,nS]=newtont('test9',[1 1],1,'gtest9',[],[-6 -6],[6 6]) ??? Error using ==> figure Argument must be a valid figure handle. Error in ==> v:\cursos\pos\otimiza\aulas\newtont.m On line 58 ==> figure(abs(ip)); [xo,Ot,nS]=newtont('test9',[1 1],'gtest9',1,[],[-6 -6],[6 6]) Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... xo = 3.0000 2.0000 Ot = 6.2644e-014 nS = 7 edit newton_h disp(sprintf('%d',feature('SessionTool'))) 0 ; dbstatus dbstack dbstack ; disp(which('newton_h')); v:\cursos\pos\otimiza\aulas\newton_h.m mdbstatus 'v:\cursos\pos\otimiza\aulas\newton_h.m' eval( 'if exist(''evaluations'',''var''), mauifunc(evaluations), end', ''); eval( 'if exist(''eye'',''var''), mauifunc(eye), end', ''); eval( 'if exist(''color'',''var''), mauifunc(color), end', ''); eval( 'if exist(''sparse'',''var''), mauifunc(sparse), end', ''); disp(which('newton_h')); v:\cursos\pos\otimiza\aulas\newton_h.m clear 'v:\cursos\pos\otimiza\aulas\newton_h.m' eval( 'if exist(''ones'',''var''), mauifunc(ones), end', ''); eval( 'if exist(''x0'',''var''), mauifunc(x0), end', ''); eval( 'if exist(''feval'',''var''), mauifunc(feval), end', ''); eval( 'if exist(''stepsize'',''var''), mauifunc(stepsize), end', ''); eval( 'if exist(''y0'',''var''), mauifunc(y0), end', ''); eval( 'if exist(''nS'',''var''), mauifunc(nS), end', ''); 7 eval( 'if exist(''while'',''var''), mauifunc(while), end', ''); eval( 'if exist(''norm'',''var''), mauifunc(norm), end', ''); cd(cd);clear functions [xo,Ot,nS]=newton_h('test9',[1 1],1,'gtest9',[],[-6 -6],[6 6]) Pause: hit any key to continue... ans = 1.0e+003 * 1.0293 1.0067 Pause: hit any key to continue... ans = 1.0e+003 * 1.0288 1.0060 Pause: hit any key to continue... ans = 1.0e+003 * 1.0283 1.0053 Pause: hit any key to continue... ans = 1.0e+003 * 1.0278 1.0046 Pause: hit any key to continue... ans = 1.0e+003 * 1.0273 1.0039 Pause: hit any key to continue... ans = 1.0e+003 * 1.0267 1.0032 Pause: hit any key to continue... ans = 1.0e+003 * 1.0261 1.0024 Pause: hit any key to continue... ans = 1.0e+003 * 1.0256 1.0016 Pause: hit any key to continue... ans = 1.0e+003 * 1.0250 1.0009 Pause: hit any key to continue... ans = 1.0e+003 * 1.0243 1.0001 Pause: hit any key to continue... ans = 1.0e+003 * 1.0237 0.9993 Pause: hit any key to continue... ans = 1.0e+003 * 1.0231 0.9985 Pause: hit any key to continue... ans = 1.0e+003 * 1.0224 0.9977 Pause: hit any key to continue... ans = 1.0e+003 * 1.0218 0.9968 Pause: hit any key to continue... ans = 1.0e+003 * 1.0211 0.9960 Pause: hit any key to continue... ans = 1.0e+003 * 1.0204 0.9951 Pause: hit any key to continue... ans = 1.0e+003 * 1.0197 0.9942 Pause: hit any key to continue... ans = 1.0e+003 * 1.0190 0.9934 Pause: hit any key to continue... ans = 1.0e+003 * 1.0183 0.9925 Pause: hit any key to continue... ans = 1.0e+003 * 1.0175 0.9916 Pause: hit any key to continue... ans = 1.0e+003 * 1.0168 0.9907 Pause: hit any key to continue... ans = 1.0e+003 * 1.0160 0.9897 Pause: hit any key to continue... ans = 1.0e+003 * 1.0152 0.9888 Pause: hit any key to continue... ans = 1.0e+003 * 1.0145 0.9879 Pause: hit any key to continue... ans = 1.0e+003 * 1.0137 0.9869 Pause: hit any key to continue... ans = 1.0e+003 * 1.0129 0.9859 Pause: hit any key to continue... ans = 1.0e+003 * 1.0121 0.9850 Pause: hit any key to continue... ans = 1.0e+003 * 1.0113 0.9840 Pause: hit any key to continue... ans = 1.0e+003 * 1.0104 0.9830 Pause: hit any key to continue... ans = 1.0e+003 * 1.0096 0.9820 Pause: hit any key to continue... ans = 1.0e+003 * 1.0088 0.9810 Pause: hit any key to continue... ans = 1.0e+003 * 1.0080 0.9800 Pause: hit any key to continue... ans = 1.0e+003 * 1.0071 0.9790 Pause: hit any key to continue... ans = 1.0e+003 * 1.0063 0.9780 Pause: hit any key to continue... ans = 1.0e+003 * 1.0055 0.9770 Pause: hit any key to continue... ans = 1.0e+003 * 1.0047 0.9760 Pause: hit any key to continue... ans = 1.0e+003 * 1.0038 0.9750 Pause: hit any key to continue... ans = 1.0e+003 * 1.0030 0.9739 Pause: hit any key to continue... ans = 1.0e+003 * 1.0022 0.9729 Pause: hit any key to continue... ans = 1.0e+003 * 1.0014 0.9719 Pause: hit any key to continue... ans = 1.0e+003 * 1.0006 0.9709 Pause: hit any key to continue... ans = 999.7561 969.8305 Pause: hit any key to continue... ans = 998.9583 968.7991 Pause: hit any key to continue... ans = 998.1685 967.7682 Pause: hit any key to continue... ans = 997.3872 966.7386 Pause: hit any key to continue... ans = 996.6154 965.7108 Pause: hit any key to continue... ans = 995.8537 964.6855 Pause: hit any key to continue... ans = 963.6633 995.1027 Pause: hit any key to continue... ans = 962.6450 994.3632 Pause: hit any key to continue... ans = 961.6312 993.6357 Pause: hit any key to continue... Warning Newton: reached maximum number of iterations! xo = 2.2194 1.8082 Ot = 20.4814 nS = 101 eval( 'if exist(''norm'',''var''), mauifunc(norm), end', ''); eval( 'if exist(''problem'',''var''), mauifunc(problem), end', ''); eval( 'if exist(''d'',''var''), mauifunc(d), end', ''); disp(which('newton_h')); v:\cursos\pos\otimiza\aulas\newton_h.m clear 'v:\cursos\pos\otimiza\aulas\newton_h.m' ; quit