type test19 function S=test(x) % Papageorgiou, 1996 % % x0 = 2 % goals: S* = [0.5 0.5]' % weights: w = [0.5 0.5]' % xo = 0.1429 % S(xo) = [1.0102 1.0102]' %w=0.5; global w S=w*(1+0.5*x.^2)+(1-w)*(4*(x-0.5).^2+0.5); % [x,S,ns]=bfgs('test19',2) global w w=0.5 w = 0.5000 [x,S,ns]=bfgs('test19',2) Directional Iteration Func-count f(x) Step-size derivative 1 1 6.25 0.255102 -49 2 6 0.805556 0.222222 0 Optimization terminated successfully: Search direction less than 2*options.TolX x = 0.4444 S = 0.8056 ns = 7 what M-files in the current directory V:\Cursos\Pos\Otimiza\Aulas CATALIS gmilp1 htest4 restr24eq EXTRATOR gminlp1 htest9 rosembr LUCRO gminlp2 interior set1 MINQUA gminlp3 karmarkar setoptim MODELO gminlp4 lmarqua sol_extrat Minqua44 gminlp5 lp_nlp sqp Modelo44 gminlp6 milp steepdes OPT_RES gmodelagem milp1 swarm ObjFunSa gmurray milprog test0 PLANOS grad minlp test1 READ2 grestr1 minlp1 test10 SEMIDEF grestr14 minlp2 test11 SMODELO grestr14eq minlp3 test12 ShowData grestr15 minlp4 test13 aurea grestr16 minlp5 test14 bandem1 grestr17 minlp6 test15 bfgs grestr20 minlpn test16 bracket grestr21 modelagem test17 buscarnd grestr23 naturais test18 cgrad grestr24 newton test19 checkbounds grestr24eq newton_h test1gn coggins grg newton_mod test1m compdir grg_ml newtont test2 complex gtest1 nlconst test20 dados_ex6_44 gtest10 nlp_internal test21 dfp gtest12 pareto18 test22 dual gtest13 pareto19 test23 ex2_karm gtest14 pareto20 test24 ex_karma gtest14eq pareto21 test3 ex_qp1 gtest16 powell test4 ex_qp2 gtest17 qpsub test5 ex_qp3 gtest2 refino test6 ex_swarm gtest20 restr test7 exmilp gtest21 restr1 test8 exmilp2 gtest23 restr14 test9 exmilprog gtest24 restr14eq teste_buscarnd exmilprog2 gtest24eq restr15 univar extrat gtest8 restr16 varmetr fmincon1 gtest9 restr17 visual fminunc1 hkjeeves restr20 writearq fminusub htest1 restr21 xplot fun htest10 restr23 func44 htest2 restr24 type pareto19 % Papageorgiou, 1996 % % x0 = 2 % goals: S* = [0.5 0.5]' % weights: w = [0.5 0.5]' % xo = 0.1429 % S(xo) = [1.0102 1.0102]' %w=0.5; global w xo=[]; So=[]; F1=[]; F2=[]; for w=0:0.01:1 [x,S,ns]=bfgs('test19',2); xo=[xo x]; So=[So S]; F1=[F1 1+0.5*x.^2]; F2=[F2 4*(x-0.5).^2+0.5]; end w=[0:0.01:1]; pareto19 Directional Iteration Func-count f(x) Step-size derivative 1 1 9.5 0.131944 -144 2 6 0.5 0.125 -6.66e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 9.435 0.133253 -142 2 6 0.506248 0.126103 0 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 9.37 0.134588 -139 2 6 0.512494 0.127226 -3.93e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 9.305 0.135949 -137 2 6 0.518736 0.12837 -1.3e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 9.24 0.137337 -135 2 6 0.524974 0.129534 -6.44e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 9.175 0.138752 -132 2 6 0.531209 0.130719 1.28e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 9.11 0.140197 -130 2 6 0.537441 0.131926 1.27e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 9.045 0.141671 -128 2 6 0.543668 0.133156 0 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 8.98 0.143176 -125 2 6 0.549892 0.134409 -8.7e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 8.915 0.144712 -123 2 6 0.556113 0.135685 2.46e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 8.85 0.146281 -121 2 6 0.562329 0.136986 2.44e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 8.785 0.147883 -119 2 6 0.568541 0.138313 -4.84e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 8.72 0.14952 -117 2 6 0.574749 0.139665 8.39e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 8.655 0.151192 -114 2 6 0.580952 0.141044 2.38e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 8.59 0.152901 -112 2 6 0.587151 0.14245 -1.77e-006 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 8.525 0.154649 -110 2 6 0.593345 0.143885 -1.05e-006 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 8.46 0.156435 -108 2 6 0.599535 0.145349 -6.93e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 8.395 0.158262 -106 2 6 0.60572 0.146843 -1.14e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 8.33 0.160131 -104 2 6 0.611899 0.148368 4.53e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 8.265 0.162043 -102 2 6 0.618073 0.149925 -5.61e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 8.2 0.164 -100 2 6 0.624242 0.151515 1.11e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 8.135 0.166003 -98 2 6 0.630406 0.153139 5.5e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 8.07 0.168055 -96 2 6 0.636563 0.154799 0 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 8.005 0.170156 -94.1 2 6 0.642715 0.156495 1.08e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 7.94 0.172309 -92.2 2 6 0.648861 0.158228 3.2e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 7.875 0.174515 -90.2 2 6 0.655 0.16 0 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 7.81 0.176777 -88.4 2 6 0.661133 0.161812 1.04e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 7.745 0.179096 -86.5 2 6 0.667259 0.163666 -3.1e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 7.68 0.181474 -84.6 2 6 0.673377 0.165563 -4.09e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 7.615 0.183915 -82.8 2 6 0.679489 0.167504 0 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 7.55 0.18642 -81 2 6 0.685593 0.169492 -2e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 7.485 0.188991 -79.2 2 6 0.69169 0.171527 -9.88e-008 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 7.42 0.191632 -77.4 2 6 0.697778 0.173611 -2.93e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 7.355 0.194345 -75.7 2 6 0.703858 0.175747 -9.66e-008 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 7.29 0.197134 -74 2 6 0.709929 0.177936 -6.4e-006 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 7.225 0.2 -72.2 2 6 0.715991 0.18018 -1.89e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 7.16 0.202948 -70.6 2 6 0.722044 0.182482 9.33e-008 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 7.095 0.205981 -68.9 2 6 0.728087 0.184843 0 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 7.03 0.209102 -67.2 2 6 0.73412 0.187266 5.46e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 6.965 0.212315 -65.6 2 6 0.740142 0.189753 0 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 6.9 0.215625 -64 2 6 0.746154 0.192308 1.78e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 6.835 0.219035 -62.4 2 6 0.752154 0.194932 0 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 6.77 0.222551 -60.8 2 6 0.758142 0.197628 -2.6e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 6.705 0.226176 -59.3 2 6 0.764118 0.200401 2.56e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 6.64 0.229917 -57.8 2 6 0.770081 0.203252 1.1e-006 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 6.575 0.233778 -56.2 2 6 0.776031 0.206186 0 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 6.51 0.237765 -54.8 2 6 0.781967 0.209205 1.64e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 6.445 0.241884 -53.3 2 6 0.787887 0.212314 1.62e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 6.38 0.246142 -51.8 2 6 0.793793 0.215517 1.6e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 6.315 0.250546 -50.4 2 6 0.799683 0.218818 -3.15e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 6.25 0.255102 -49 2 6 0.805556 0.222222 0 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 6.185 0.259819 -47.6 2 6 0.811411 0.225734 7.66e-008 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 6.12 0.264706 -46.2 2 6 0.817248 0.229358 -5.28e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 6.055 0.269771 -44.9 2 6 0.823065 0.2331 0 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 5.99 0.275023 -43.6 2 6 0.828863 0.236967 -2.2e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 5.925 0.280473 -42.3 2 6 0.834639 0.240964 -1.52e-006 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 5.86 0.286133 -41 2 6 0.840392 0.245098 2.13e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 5.795 0.292013 -39.7 2 6 0.846122 0.249377 -3.5e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 5.73 0.298127 -38.4 2 6 0.851827 0.253807 -2.07e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 5.665 0.304488 -37.2 2 6 0.857506 0.258398 2.71e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 5.6 0.311111 -36 2 6 0.863158 0.263158 -1.33e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 5.535 0.318012 -34.8 2 6 0.86878 0.268097 -2.62e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 5.47 0.325208 -33.6 2 6 0.874372 0.273224 -2.58e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 5.405 0.332718 -32.5 2 6 0.87993 0.278552 1.27e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 5.34 0.340561 -31.4 2 6 0.885455 0.284091 0 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 5.275 0.34876 -30.2 2 6 0.890942 0.289855 1.83e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 5.21 0.357339 -29.2 2 6 0.896391 0.295858 0 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 5.145 0.366323 -28.1 2 6 0.901798 0.302115 5.88e-008 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 5.08 0.37574 -27 2 6 0.90716 0.308642 1.73e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 5.015 0.385621 -26 2 6 0.912476 0.315457 0 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 4.95 0.396 -25 2 6 0.917742 0.322581 -1.11e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 4.885 0.406914 -24 2 6 0.922954 0.330033 -2.18e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 4.82 0.418403 -23 2 6 0.928108 0.337838 -5.33e-008 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 4.755 0.430512 -22.1 2 6 0.933201 0.346021 2.09e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 4.69 0.443289 -21.2 2 6 0.938227 0.35461 -1.02e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 4.625 0.45679 -20.3 2 6 0.943182 0.363636 -2.5e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 4.56 0.471074 -19.4 2 6 0.94806 0.373134 2.44e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 4.495 0.486209 -18.5 2 6 0.952854 0.383142 2.67e-006 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 4.43 0.502268 -17.6 2 6 0.957559 0.393701 -2.33e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 4.365 0.519334 -16.8 2 6 0.962166 0.404858 4.55e-008 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 4.3 0.5375 -16 2 6 0.966667 0.416667 0 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 4.235 0.55687 -15.2 2 6 0.971052 0.429185 -8.66e-008 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 4.17 0.577562 -14.4 2 6 0.97531 0.442478 0 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 4.105 0.599708 -13.7 2 6 0.979429 0.456621 -4.11e-008 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 4.04 0.623457 -13 2 6 0.983396 0.471698 0 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 3.975 0.64898 -12.2 2 6 0.987195 0.487805 0 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 3.91 0.676471 -11.6 2 6 0.990808 0.505051 -7.55e-008 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 3.845 0.706152 -10.9 2 6 0.994215 0.52356 -7.33e-008 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 3.78 0.738281 -10.2 2 6 0.997391 0.543478 1.07e-007 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 3.715 0.773153 -9.61 2 6 1.00031 0.564972 0 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 3.65 0.811111 -9 2 6 1.00294 0.588235 0 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 3.585 0.852556 -8.41 2 6 1.00525 0.613497 6.44e-008 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 3.52 0.897959 -7.84 2 6 1.00718 0.641026 -6.22e-008 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 3.455 0.947874 -7.29 2 6 1.00869 0.671141 6e-008 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 3.39 1 -6.76 2 6 1.00972 0.704225 5.77e-008 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 3.325 1 -6.25 2 6 1.01019 0.740741 5.55e-008 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 3.26 1 -5.76 2 6 1.01 0.78125 0 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 3.195 1 -5.29 2 6 1.00905 0.826446 0 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 3.13 1 -4.84 2 6 1.00719 0.877193 0 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 3.065 1 -4.41 2 6 1.00425 0.934579 -9.33e-008 Optimization terminated successfully: Search direction less than 2*options.TolX Directional Iteration Func-count f(x) Step-size derivative 1 1 3 1 -4 2 6 1 1 0 Optimization terminated successfully: Search direction less than 2*options.TolX plot(F1,F2) type parreto19 ??? Error using ==> type parreto19.m: File not found. type pareto19 % Papageorgiou, 1996 % % x0 = 2 % goals: S* = [0.5 0.5]' % weights: w = [0.5 0.5]' % xo = 0.1429 % S(xo) = [1.0102 1.0102]' %w=0.5; global w xo=[]; So=[]; F1=[]; F2=[]; for w=0:0.01:1 [x,S,ns]=bfgs('test19',2); xo=[xo x]; So=[So S]; F1=[F1 1+0.5*x.^2]; F2=[F2 4*(x-0.5).^2+0.5]; end w=[0:0.01:1]; figure; plot(w,x) figure; plot(w,xo) figure; plot(xo,So) figure; plot(xo,[So F1 F2]) ??? Error using ==> plot Vectors must be the same lengths. So So = Columns 1 through 7 0.5000 0.5062 0.5125 0.5187 0.5250 0.5312 0.5374 Columns 8 through 14 0.5437 0.5499 0.5561 0.5623 0.5685 0.5747 0.5810 Columns 15 through 21 0.5872 0.5933 0.5995 0.6057 0.6119 0.6181 0.6242 Columns 22 through 28 0.6304 0.6366 0.6427 0.6489 0.6550 0.6611 0.6673 Columns 29 through 35 0.6734 0.6795 0.6856 0.6917 0.6978 0.7039 0.7099 Columns 36 through 42 0.7160 0.7220 0.7281 0.7341 0.7401 0.7462 0.7522 Columns 43 through 49 0.7581 0.7641 0.7701 0.7760 0.7820 0.7879 0.7938 Columns 50 through 56 0.7997 0.8056 0.8114 0.8172 0.8231 0.8289 0.8346 Columns 57 through 63 0.8404 0.8461 0.8518 0.8575 0.8632 0.8688 0.8744 Columns 64 through 70 0.8799 0.8855 0.8909 0.8964 0.9018 0.9072 0.9125 Columns 71 through 77 0.9177 0.9230 0.9281 0.9332 0.9382 0.9432 0.9481 Columns 78 through 84 0.9529 0.9576 0.9622 0.9667 0.9711 0.9753 0.9794 Columns 85 through 91 0.9834 0.9872 0.9908 0.9942 0.9974 1.0003 1.0029 Columns 92 through 98 1.0052 1.0072 1.0087 1.0097 1.0102 1.0100 1.0090 Columns 99 through 101 1.0072 1.0043 1.0000 xo xo = Columns 1 through 7 0.5000 0.4994 0.4987 0.4981 0.4974 0.4967 0.4960 Columns 8 through 14 0.4953 0.4946 0.4939 0.4932 0.4924 0.4916 0.4908 Columns 15 through 21 0.4900 0.4892 0.4884 0.4875 0.4866 0.4858 0.4848 Columns 22 through 28 0.4839 0.4830 0.4820 0.4810 0.4800 0.4790 0.4779 Columns 29 through 35 0.4768 0.4757 0.4746 0.4734 0.4722 0.4710 0.4698 Columns 36 through 42 0.4685 0.4672 0.4658 0.4644 0.4630 0.4615 0.4600 Columns 43 through 49 0.4585 0.4569 0.4553 0.4536 0.4519 0.4501 0.4483 Columns 50 through 56 0.4464 0.4444 0.4424 0.4404 0.4382 0.4360 0.4337 Columns 57 through 63 0.4314 0.4289 0.4264 0.4238 0.4211 0.4182 0.4153 Columns 64 through 70 0.4123 0.4091 0.4058 0.4024 0.3988 0.3951 0.3912 Columns 71 through 77 0.3871 0.3828 0.3784 0.3737 0.3688 0.3636 0.3582 Columns 78 through 84 0.3525 0.3465 0.3401 0.3333 0.3262 0.3186 0.3105 Columns 85 through 91 0.3019 0.2927 0.2828 0.2723 0.2609 0.2486 0.2353 Columns 92 through 98 0.2209 0.2051 0.1879 0.1690 0.1481 0.1250 0.0992 Columns 99 through 101 0.0702 0.0374 -0.0000 figure; plot(xo',[So'; F1'; F2']) ??? Error using ==> plot Vectors must be the same lengths. figure; plot(xo',[So' F1' F2']) type pareto18 % Papageorgiou, 1996 % % x0 = 2 % goals: S* = [0.5 0.5]' % weights: w = [0.5 0.5]' % xo = 0.1429 % S(xo) = [1.0102 1.0102]' xo=[]; So=[]; F1=[]; F2=[]; gamao=[]; goal = [0.5; 0.5]; for w1=0:0.1:1 w=[w1 1-w1]; [x,S,gama,ex,out,lambda]=fgoalattain('test18',2,goal,w) xo=[xo x]; So=[So S]; gamao=[gamao gama]; F1=[F1 S(1)]; F2=[F2 S(2)]; end w=[0:0.1:1]; help fgoalattain FGOALATTAIN Solves the multi-objective goal attainment optimization problem. X = FGOALATTAIN(FUN,X0,GOAL,WEIGHT) tries to make the objective functions (F) supplied by FUN (usually an M-file: FUN.M) attain the goals (GOAL) by varying X. In doing so the following nonlinear programming problem is solved: min { LAMBDA : F(X)-WEIGHT.*LAMBDA<=GOAL } X,LAMBDA The function FUN should return the values of the objectives, F when called using feval: F=feval(FUN,X). X=FGOALATTAIN(FUN,X0,GOAL,WEIGHT,A,B) solves the goal attainment problem subject to the linear inequalities A*X <= B. X=FGOALATTAIN(FUN,X0,GOAL,WEIGHT,A,B,Aeq,Beq) solves the goal attainment problem subject to the linear equalities Aeq*X = Beq as well. X=FGOALATTAIN(FUN,X0,GOAL,WEIGHT,A,B,Aeq,Beq,LB,UB) defines a set of lower and upper bounds on the design variables, X, so that the solution is in the range LB <= X <= UB. Use empty matrices for LB and U if no bounds exist. Set LB(i) = -Inf if X(i) is unbounded below; set UB(i) = Inf if X(i) is unbounded above. X=FGOALATTAIN(FUN,X0,GOAL,WEIGHT,A,B,Aeq,Beq,LB,UB,NONLCON) subjects the goal attainment problem to the constraints defined in NONLCON (usually an M-file: NONLCON.m). The function NONLCON should return the vectors C and Ceq, representing the nonlinear inequalities and equalities respectively, when called with feval: [C, Ceq] = feval(NONLCON,X). FGOALATTAIN optimizes such that C(X)<=0 and Ceq(X)=0. X=FGOALATTAIN(FUN,X0,GOAL,WEIGHT,A,B,Aeq,Beq,LB,UB,NONLCON,OPTIONS) minimizes the with default optimization parameters replaced by values in the structure OPTIONS, an argument created with the OPTIMSET function. See OPTIMSET for details. Used options are Display, TolX, TolFun, TolCon, DerivativeCheck, GradObj, GradConstr, MaxFunEvals, MaxIter, MeritFunction, GoalsExactAchieve, Diagnostics, DiffMinChange, and DiffMaxChange. Use the GradObj option to specify that FUN may be called with two output arguments where the second, G, is the partial derivatives of the function df/dX, at the point X: [F,G] = feval(FUN,X). Use the GradConstr option to specify that NONLCON may be called with four output arguments: [C,Ceq,GC,GCeq] = feval(NONLCON,X) where GC is the partial derivatives of the constraint vector of inequalities C an GCeq is the partial derivatives of the constraint vector of equalities Ceq. Use OPTIONS = [] as a place holder if no options are set. X=FGOALATTAIN(FUN,X0,GOAL,WEIGHT,A,B,Aeq,Beq,LB,UB,NONLCON,OPTIONS,P1,P2,...) passes the problem-dependent parameters P1,P2,... directly to the functions FUN and NONLCON: feval(FUN,X,P1,P2,...) and feval(NONLCON,X,P1,P2,...). Pass empty matrices for A, B, Aeq, Beq, LB, UB, NONLCON and OPTIONS to use the default values. [X,FVAL]=FGOALATTAIN(FUN,X0,...) returns the value of the objective function FUN at the solution X. [X,FVAL,ATTAINFACTOR]=FGOALATTAIN(FUN,X0,...) returns the attainment factor at the solution X. If ATTAINFACTOR is negative, the goals have been over- achieved; if ATTAINFACTOR is positive, the goals have been under-achieved. [X,FVAL,ATTAINFACTOR,EXITFLAG]=FGOALATTAIN(FUN,X0,...) returns a string EXITFLAG that describes the exit condition of FGOALATTAIN. If EXITFLAG is: > 0 then FGOALATTAIN converged to a solution X. 0 then the maximum number of function evaluations was reached. < 0 then FGOALATTAIN did not converge to a solution. [X,FVAL,ATTAINFACTOR,EXITFLAG,OUTPUT]=FGOALATTAIN(FUN,X0,...) returns a structure OUTPUT with the number of iterations taken in OUTPUT.iterations, the number of function evaluations in OUTPUT.funcCount, and the algorithm used in OUTPUT.algorithm. [X,FVAL,ATTAINFACTOR,EXITFLAG,OUTPUT,LAMBDA]=FGOALATTAIN(FUN,X0,...) returns the Lagrange multiplier at the solution X: LAMBDA.lower for LB, LAMBDA.upper for UB, LAMBDA.ineqlin is for the linear inequalities, LAMBDA.eqlin is for the linear equalities, LAMBDA.ineqnonlin is for the nonlinear inequalities, and LAMBDA.eqnonlin is for the nonlinear equalities. For more details, type the M-file FGOALATTAIN.M. See also OPTIMSET, OPTIMGET. type pareto18 % Papageorgiou, 1996 % % x0 = 2 % goals: S* = [0.5 0.5]' % weights: w = [0.5 0.5]' % xo = 0.1429 % S(xo) = [1.0102 1.0102]' xo=[]; So=[]; F1=[]; F2=[]; gamao=[]; goal = [0.5; 0.5]; for w1=0:0.1:1 w=[w1 1-w1]; [x,S,gama,ex,out,lambda]=fgoalattain('test18',2,goal,w) xo=[xo x]; So=[So S]; gamao=[gamao gama]; F1=[F1 S(1)]; F2=[F2 S(2)]; end w=[0:0.1:1]; type test18 function S=test(x) % Papageorgiou, 1996 % % x0 = 2 % goals: S* = [0.5 0.5]' % weights: w = [0.5 0.5]' % xo = 0.1429 % S(xo) = [1.0102 1.0102]' S(1)=1+0.5*x.^2; S(2)=4*(x-0.5).^2+0.5; % goal = [0.5; 0.5]; % w = abs(goal); % [x,S,gama,ex,out,lambda]=fgoalattain('test18',2,goal,w) goal = [0.5; 0.5]; w = abs(goal); [x,S,gama,ex,out,lambda]=fgoalattain('test18',2,goal,w) Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 2 x = 0.1429 S = 1.0102 1.0102 gama = 1.0204 ex = 1 out = iterations: 5 funcCount: 22 stepsize: 1 algorithm: 'goal attainment SQP, Quasi-Newton, line_search' firstorderopt: [] cgiterations: [] lambda = lower: 0 upper: 0 eqlin: [0x1 double] eqnonlin: [0x1 double] ineqlin: [0x1 double] ineqnonlin: [0x1 double] type pareto18 % Papageorgiou, 1996 % % x0 = 2 % goals: S* = [0.5 0.5]' % weights: w = [0.5 0.5]' % xo = 0.1429 % S(xo) = [1.0102 1.0102]' xo=[]; So=[]; F1=[]; F2=[]; gamao=[]; goal = [0.5; 0.5]; for w1=0:0.1:1 w=[w1 1-w1]; [x,S,gama,ex,out,lambda]=fgoalattain('test18',2,goal,w) xo=[xo x]; So=[So S]; gamao=[gamao gama]; F1=[F1 S(1)]; F2=[F2 S(2)]; end w=[0:0.1:1]; pareto18 Maximum number of function evaluations exceeded; increase OPTIONS.MaxFunEvals x = 0.0770 S = 1.0030 1.2157 gama = -0.3797 ex = 0 out = iterations: 41 funcCount: 202 stepsize: 2 algorithm: 'goal attainment SQP, Quasi-Newton, line_search' firstorderopt: [] cgiterations: [] lambda = lower: 0 upper: 0 eqlin: [0x1 double] eqnonlin: [0x1 double] ineqlin: [0x1 double] ineqnonlin: [0x1 double] Optimization terminated successfully: Magnitude of directional derivative in search direction less than 2*options.TolFun and maximum constraint violation is less than options.TolCon Active Constraints: 1 x = -1.4523e-008 S = 1.0000 1.5000 gama = 5.0000 ex = 1 out = iterations: 6 funcCount: 38 stepsize: 0.0020 algorithm: 'goal attainment SQP, Quasi-Newton, line_search' firstorderopt: [] cgiterations: [] lambda = lower: 0 upper: 0 eqlin: [0x1 double] eqnonlin: [0x1 double] ineqlin: [0x1 double] ineqnonlin: [0x1 double] Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 x = -1.4624e-008 S = 1.0000 1.5000 gama = 2.5000 ex = 1 out = iterations: 6 funcCount: 38 stepsize: 9.7656e-004 algorithm: 'goal attainment SQP, Quasi-Newton, line_search' firstorderopt: [] cgiterations: [] lambda = lower: 0 upper: 0 eqlin: [0x1 double] eqnonlin: [0x1 double] ineqlin: [0x1 double] ineqnonlin: [0x1 double] Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 x = -6.1019e-009 S = 1.0000 1.5000 gama = 1.6667 ex = 1 out = iterations: 5 funcCount: 25 stepsize: 0.1250 algorithm: 'goal attainment SQP, Quasi-Newton, line_search' firstorderopt: [] cgiterations: [] lambda = lower: 0 upper: 0 eqlin: [0x1 double] eqnonlin: [0x1 double] ineqlin: [0x1 double] ineqnonlin: [0x1 double] Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 2 x = 0.0660 S = 1.0022 1.2533 gama = 1.2555 ex = 1 out = iterations: 7 funcCount: 30 stepsize: 1 algorithm: 'goal attainment SQP, Quasi-Newton, line_search' firstorderopt: [] cgiterations: [] lambda = lower: 0 upper: 0 eqlin: [0x1 double] eqnonlin: [0x1 double] ineqlin: [0x1 double] ineqnonlin: [0x1 double] Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 2 x = 0.1429 S = 1.0102 1.0102 gama = 1.0204 ex = 1 out = iterations: 5 funcCount: 22 stepsize: 1 algorithm: 'goal attainment SQP, Quasi-Newton, line_search' firstorderopt: [] cgiterations: [] lambda = lower: 0 upper: 0 eqlin: [0x1 double] eqnonlin: [0x1 double] ineqlin: [0x1 double] ineqnonlin: [0x1 double] Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 2 x = 0.2053 S = 1.0211 0.8474 gama = 0.8685 ex = 1 out = iterations: 7 funcCount: 29 stepsize: 1 algorithm: 'goal attainment SQP, Quasi-Newton, line_search' firstorderopt: [] cgiterations: [] lambda = lower: 0 upper: 0 eqlin: [0x1 double] eqnonlin: [0x1 double] ineqlin: [0x1 double] ineqnonlin: [0x1 double] Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 2 x = 0.2608 S = 1.0340 0.7289 gama = 0.7629 ex = 1 out = iterations: 7 funcCount: 29 stepsize: 1 algorithm: 'goal attainment SQP, Quasi-Newton, line_search' firstorderopt: [] cgiterations: [] lambda = lower: 0 upper: 0 eqlin: [0x1 double] eqnonlin: [0x1 double] ineqlin: [0x1 double] ineqnonlin: [0x1 double] Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 2 x = 0.3147 S = 1.0495 0.6374 gama = 0.6869 ex = 1 out = iterations: 8 funcCount: 33 stepsize: 1 algorithm: 'goal attainment SQP, Quasi-Newton, line_search' firstorderopt: [] cgiterations: [] lambda = lower: 0 upper: 0 eqlin: [0x1 double] eqnonlin: [0x1 double] ineqlin: [0x1 double] ineqnonlin: [0x1 double] Optimization terminated successfully: Magnitude of directional derivative in search direction less than 2*options.TolFun and maximum constraint violation is less than options.TolCon Active Constraints: 1 2 x = 0.3742 S = 1.0700 0.5633 gama = 0.6333 ex = 1 out = iterations: 7 funcCount: 29 stepsize: 1 algorithm: 'goal attainment SQP, Quasi-Newton, line_search' firstorderopt: [] cgiterations: [] lambda = lower: 0 upper: 0 eqlin: [0x1 double] eqnonlin: [0x1 double] ineqlin: [0x1 double] ineqnonlin: [0x1 double] Optimization terminated successfully: Magnitude of directional derivative in search direction less than 2*options.TolFun and maximum constraint violation is less than options.TolCon Active Constraints: 1 2 x = 0.5000 S = 1.1250 0.5000 gama = 0.6250 ex = 1 out = iterations: 20 funcCount: 84 stepsize: 1 algorithm: 'goal attainment SQP, Quasi-Newton, line_search' firstorderopt: [] cgiterations: [] lambda = lower: 0 upper: 0 eqlin: [0x1 double] eqnonlin: [0x1 double] ineqlin: [0x1 double] ineqnonlin: [0x1 double] type pareto18 % Papageorgiou, 1996 % % x0 = 2 % goals: S* = [0.5 0.5]' % weights: w = [0.5 0.5]' % xo = 0.1429 % S(xo) = [1.0102 1.0102]' xo=[]; So=[]; F1=[]; F2=[]; gamao=[]; goal = [0.5; 0.5]; for w1=0:0.1:1 w=[w1 1-w1]; [x,S,gama,ex,out,lambda]=fgoalattain('test18',2,goal,w) xo=[xo x]; So=[So S]; gamao=[gamao gama]; F1=[F1 S(1)]; F2=[F2 S(2)]; end w=[0:0.1:1]; figure(1); plot(F1,F2) figure(3); plot(w,x) figure(3); plot(w,xo) what M-files in the current directory V:\Cursos\Pos\Otimiza\Aulas CATALIS gmilp1 htest4 restr24eq EXTRATOR gminlp1 htest9 rosembr LUCRO gminlp2 interior set1 MINQUA gminlp3 karmarkar setoptim MODELO gminlp4 lmarqua sol_extrat Minqua44 gminlp5 lp_nlp sqp Modelo44 gminlp6 milp steepdes OPT_RES gmodelagem milp1 swarm ObjFunSa gmurray milprog test0 PLANOS grad minlp test1 READ2 grestr1 minlp1 test10 SEMIDEF grestr14 minlp2 test11 SMODELO grestr14eq minlp3 test12 ShowData grestr15 minlp4 test13 aurea grestr16 minlp5 test14 bandem1 grestr17 minlp6 test15 bfgs grestr20 minlpn test16 bracket grestr21 modelagem test17 buscarnd grestr23 naturais test18 cgrad grestr24 newton test19 checkbounds grestr24eq newton_h test1gn coggins grg newton_mod test1m compdir grg_ml newtont test2 complex gtest1 nlconst test20 dados_ex6_44 gtest10 nlp_internal test21 dfp gtest12 pareto18 test22 dual gtest13 pareto19 test23 ex2_karm gtest14 pareto20 test24 ex_karma gtest14eq pareto21 test3 ex_qp1 gtest16 powell test4 ex_qp2 gtest17 qpsub test5 ex_qp3 gtest2 refino test6 ex_swarm gtest20 restr test7 exmilp gtest21 restr1 test8 exmilp2 gtest23 restr14 test9 exmilprog gtest24 restr14eq teste_buscarnd exmilprog2 gtest24eq restr15 univar extrat gtest8 restr16 varmetr fmincon1 gtest9 restr17 visual fminunc1 hkjeeves restr20 writearq fminusub htest1 restr21 xplot fun htest10 restr23 func44 htest2 restr24 type pareto20 % Papageorgiou, 1996 % % x0 = 2 % goals: S* = [0.5 0.5]' % weights: w = [0.5 0.5]' % xo = 0.1429 % S(xo) = [1.0102 1.0102]' global e xo=[]; So=[]; F1=[]; F2=[]; for e=1:0.01:1.125 [x,S,ns,lambda]=sqp('test20','restr20',2); xo=[xo x]; So=[So S]; F1=[F1 1+0.5*x.^2]; F2=[F2 4*(x-0.5).^2+0.5]; end e=[1:0.01:1.125]; type 20 ??? Error using ==> type 20.m: File not found. type test20 function S=test(x) % Papageorgiou, 1996 % % x0 = 2 % xo = 0.1429 % S(xo) = [1.0102 1.0102]' S=4*(x-0.5).^2+0.5; % [x,S,nS,lambda]=sqp('test20','restr20',2) type restr20 function [g,h]=restr(x) % Papageorgiou, 1996 % % x0 = 2 % goals: S* = [0.5 0.5]' % weights: w = [0.5 0.5]' % xo = 0.1429 % S(xo) = [1.0102 1.0102]' %e=1.1; global e g(1)=1+0.5*x.^2-e; g(2)=-x; h=[]; % [x,S,ns,lambda]=sqp('test20','restr20',2) global e type test20 function S=test(x) % Papageorgiou, 1996 % % x0 = 2 % xo = 0.1429 % S(xo) = [1.0102 1.0102]' S=4*(x-0.5).^2+0.5; % [x,S,nS,lambda]=sqp('test20','restr20',2) e=1 e = 1 [x,S,nS,lambda]=sqp('test20','restr20',2) max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 2 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 0.125 1 -2.22e-008 4 11 0.75 0.03125 1 0.375 5 14 1.16016 0.004395 1 0.152 6 17 1.32129 0.001099 1 0.085 7 20 1.40845 0.0002747 1 0.0447 8 23 1.45367 6.866e-005 1 0.0229 9 26 1.4767 1.717e-005 1 0.0116 10 29 1.48832 4.292e-006 1 0.00583 11 32 1.49415 1.073e-006 1 0.00292 12 35 1.49707 2.682e-007 1 0.00146 13 38 1.49854 6.706e-008 1 0.000732 Hessian modified 14 41 1.49927 1.676e-008 1 0.000366 Hessian modified 15 44 1.49963 4.192e-009 1 0.000183 Hessian modified 16 47 1.49982 1.048e-009 1 9.16e-005 Hessian modified 17 50 1.49991 2.62e-010 1 4.58e-005 Hessian modified 18 53 1.49995 6.551e-011 1 2.29e-005 Hessian modified 19 56 1.49998 1.641e-011 1 1.15e-005 Hessian modified 20 59 1.49999 4.102e-012 1 5.73e-006 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 x = 1.4322e-006 S = 1.5000 nS = 61 lambda = lower: 0 upper: 0 eqlin: [0x1 double] eqnonlin: [0x1 double] ineqlin: [0x1 double] ineqnonlin: [2x1 double] e=2 e = 2 [x,S,nS,lambda]=sqp('test20','restr20',2) max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.5 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints x = 0.5000 S = 0.5000 nS = 10 lambda = lower: 0 upper: 0 eqlin: [0x1 double] eqnonlin: [0x1 double] ineqlin: [0x1 double] ineqnonlin: [2x1 double] e=1.125 e = 1.1250 [x,S,nS,lambda]=sqp('test20','restr20',2) max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.875 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 2.819e-009 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints x = 0.5000 S = 0.5000 nS = 10 lambda = lower: 0 upper: 0 eqlin: [0x1 double] eqnonlin: [0x1 double] ineqlin: [0x1 double] ineqnonlin: [2x1 double] e=1.1 e = 1.1000 [x,S,nS,lambda]=sqp('test20','restr20',2) max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.9 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 0.025 1 -4.44e-009 4 11 0.51 0.00125 1 0.0025 5 14 0.511289 -0.0001514 1 -0.000144 Hessian modified twice 6 17 0.511146 5.736e-008 1 5.42e-008 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 x = 0.4472 S = 0.5111 nS = 19 lambda = lower: 0 upper: 0 eqlin: [0x1 double] eqnonlin: [0x1 double] ineqlin: [0x1 double] ineqnonlin: [2x1 double] type pareto20 % Papageorgiou, 1996 % % x0 = 2 % goals: S* = [0.5 0.5]' % weights: w = [0.5 0.5]' % xo = 0.1429 % S(xo) = [1.0102 1.0102]' global e xo=[]; So=[]; F1=[]; F2=[]; for e=1:0.01:1.125 [x,S,ns,lambda]=sqp('test20','restr20',2); xo=[xo x]; So=[So S]; F1=[F1 1+0.5*x.^2]; F2=[F2 4*(x-0.5).^2+0.5]; end e=[1:0.01:1.125]; pareto20 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 2 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 0.125 1 -2.22e-008 4 11 0.75 0.03125 1 0.375 5 14 1.16016 0.004395 1 0.152 6 17 1.32129 0.001099 1 0.085 7 20 1.40845 0.0002747 1 0.0447 8 23 1.45367 6.866e-005 1 0.0229 9 26 1.4767 1.717e-005 1 0.0116 10 29 1.48832 4.292e-006 1 0.00583 11 32 1.49415 1.073e-006 1 0.00292 12 35 1.49707 2.682e-007 1 0.00146 13 38 1.49854 6.706e-008 1 0.000732 Hessian modified 14 41 1.49927 1.676e-008 1 0.000366 Hessian modified 15 44 1.49963 4.192e-009 1 0.000183 Hessian modified 16 47 1.49982 1.048e-009 1 9.16e-005 Hessian modified 17 50 1.49991 2.62e-010 1 4.58e-005 Hessian modified 18 53 1.49995 6.551e-011 1 2.29e-005 Hessian modified 19 56 1.49998 1.641e-011 1 1.15e-005 Hessian modified 20 59 1.49999 4.102e-012 1 5.73e-006 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.99 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 0.115 1 -2.04e-008 4 11 0.7116 0.02645 1 0.269 5 14 0.990637 0.001216 1 0.0227 6 17 1.01365 3.296e-005 1 0.000667 7 20 1.01431 2.707e-008 1 5.49e-007 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.98 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 0.105 1 -1.87e-008 4 11 0.6764 0.02205 1 0.191 5 14 0.864514 -0.0003732 1 -0.00455 6 17 0.859979 1.774e-006 1 2.13e-005 Hessian modified 7 20 0.86 3.923e-011 1 4.71e-010 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.97 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 0.095 1 -1.69e-008 4 11 0.6444 0.01805 1 0.133 5 14 0.769201 -0.001061 1 -0.00916 6 17 0.760123 9.732e-006 1 8.1e-005 Hessian modified 7 20 0.760204 7.884e-010 1 6.57e-009 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.96 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 0.085 1 -1.51e-008 4 11 0.6156 0.01445 1 0.0908 5 14 0.696439 -0.001249 1 -0.00795 6 17 0.688567 1.006e-005 1 6.18e-005 Hessian modified 7 20 0.688629 6.324e-010 1 3.88e-009 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.95 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 0.075 1 -1.33e-008 4 11 0.59 0.01125 1 0.06 5 14 0.640625 -0.001172 1 -0.00562 Hessian modified twice 6 17 0.635056 7.031e-006 1 3.27e-005 Hessian modified 7 20 0.635089 2.47e-010 1 1.15e-009 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.94 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 0.065 1 -1.15e-008 4 11 0.5676 0.00845 1 0.038 5 14 0.597852 -0.0009717 1 -0.00354 Hessian modified twice 6 17 0.594345 3.999e-006 1 1.42e-005 Hessian modified 7 20 0.594359 6.642e-011 1 2.36e-010 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.93 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 0.055 1 -9.77e-009 4 11 0.5484 0.00605 1 0.0228 5 14 0.565325 -0.0007314 1 -0.00201 Hessian modified twice 6 17 0.563332 1.931e-006 1 5.19e-006 Hessian modified 7 20 0.563337 1.322e-011 1 3.56e-011 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.92 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 0.045 1 -7.99e-009 4 11 0.5324 0.00405 1 0.0126 5 14 0.541006 -0.0004992 1 -0.00101 Hessian modified twice 6 17 0.539998 7.837e-007 1 1.57e-006 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.91 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 0.035 1 -6.22e-009 4 11 0.5196 0.00245 1 0.00619 5 14 0.523377 -0.0003016 1 -0.000435 Hessian modified twice 6 17 0.522943 2.535e-007 1 3.62e-007 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.9 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 0.025 1 -4.44e-009 4 11 0.51 0.00125 1 0.0025 5 14 0.511289 -0.0001514 1 -0.000144 Hessian modified twice 6 17 0.511146 5.736e-008 1 5.42e-008 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.89 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 0.015 1 -2.66e-009 4 11 0.5036 0.00045 1 0.000686 5 14 0.503862 -5.3e-005 1 -2.81e-005 Hessian modified twice 6 17 0.503834 6.385e-009 1 3.37e-009 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.88 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 0.005 1 -8.88e-010 4 11 0.5004 5e-005 1 5.45e-005 5 14 0.500409 -5.675e-006 1 -9.37e-007 Hessian modified twice Optimization terminated successfully: Magnitude of directional derivative in search direction less than 2*options.TolFun and maximum constraint violation is less than options.TolCon Active Constraints: 1 figure(1) plot(F1,F2) pareto20 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 2 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 0.125 1 -2.22e-008 4 11 0.75 0.03125 1 0.375 5 14 1.16016 0.004395 1 0.152 6 17 1.32129 0.001099 1 0.085 7 20 1.40845 0.0002747 1 0.0447 8 23 1.45367 6.866e-005 1 0.0229 9 26 1.4767 1.717e-005 1 0.0116 10 29 1.48832 4.292e-006 1 0.00583 11 32 1.49415 1.073e-006 1 0.00292 12 35 1.49707 2.682e-007 1 0.00146 13 38 1.49854 6.706e-008 1 0.000732 Hessian modified 14 41 1.49927 1.676e-008 1 0.000366 Hessian modified 15 44 1.49963 4.192e-009 1 0.000183 Hessian modified 16 47 1.49982 1.048e-009 1 9.16e-005 Hessian modified 17 50 1.49991 2.62e-010 1 4.58e-005 Hessian modified 18 53 1.49995 6.551e-011 1 2.29e-005 Hessian modified 19 56 1.49998 1.641e-011 1 1.15e-005 Hessian modified 20 59 1.49999 4.102e-012 1 5.73e-006 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.99 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 0.115 1 -2.04e-008 4 11 0.7116 0.02645 1 0.269 5 14 0.990637 0.001216 1 0.0227 6 17 1.01365 3.296e-005 1 0.000667 7 20 1.01431 2.707e-008 1 5.49e-007 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.98 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 0.105 1 -1.87e-008 4 11 0.6764 0.02205 1 0.191 5 14 0.864514 -0.0003732 1 -0.00455 6 17 0.859979 1.774e-006 1 2.13e-005 Hessian modified 7 20 0.86 3.923e-011 1 4.71e-010 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.97 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 0.095 1 -1.69e-008 4 11 0.6444 0.01805 1 0.133 5 14 0.769201 -0.001061 1 -0.00916 6 17 0.760123 9.732e-006 1 8.1e-005 Hessian modified 7 20 0.760204 7.884e-010 1 6.57e-009 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.96 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 0.085 1 -1.51e-008 4 11 0.6156 0.01445 1 0.0908 5 14 0.696439 -0.001249 1 -0.00795 6 17 0.688567 1.006e-005 1 6.18e-005 Hessian modified 7 20 0.688629 6.324e-010 1 3.88e-009 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.95 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 0.075 1 -1.33e-008 4 11 0.59 0.01125 1 0.06 5 14 0.640625 -0.001172 1 -0.00562 Hessian modified twice 6 17 0.635056 7.031e-006 1 3.27e-005 Hessian modified 7 20 0.635089 2.47e-010 1 1.15e-009 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.94 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 0.065 1 -1.15e-008 4 11 0.5676 0.00845 1 0.038 5 14 0.597852 -0.0009717 1 -0.00354 Hessian modified twice 6 17 0.594345 3.999e-006 1 1.42e-005 Hessian modified 7 20 0.594359 6.642e-011 1 2.36e-010 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.93 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 0.055 1 -9.77e-009 4 11 0.5484 0.00605 1 0.0228 5 14 0.565325 -0.0007314 1 -0.00201 Hessian modified twice 6 17 0.563332 1.931e-006 1 5.19e-006 Hessian modified 7 20 0.563337 1.322e-011 1 3.56e-011 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.92 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 0.045 1 -7.99e-009 4 11 0.5324 0.00405 1 0.0126 5 14 0.541006 -0.0004992 1 -0.00101 Hessian modified twice 6 17 0.539998 7.837e-007 1 1.57e-006 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.91 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 0.035 1 -6.22e-009 4 11 0.5196 0.00245 1 0.00619 5 14 0.523377 -0.0003016 1 -0.000435 Hessian modified twice 6 17 0.522943 2.535e-007 1 3.62e-007 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.9 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 0.025 1 -4.44e-009 4 11 0.51 0.00125 1 0.0025 5 14 0.511289 -0.0001514 1 -0.000144 Hessian modified twice 6 17 0.511146 5.736e-008 1 5.42e-008 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.89 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 0.015 1 -2.66e-009 4 11 0.5036 0.00045 1 0.000686 5 14 0.503862 -5.3e-005 1 -2.81e-005 Hessian modified twice 6 17 0.503834 6.385e-009 1 3.37e-009 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.88 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 0.005 1 -8.88e-010 4 11 0.5004 5e-005 1 5.45e-005 5 14 0.500409 -5.675e-006 1 -9.37e-007 Hessian modified twice Optimization terminated successfully: Magnitude of directional derivative in search direction less than 2*options.TolFun and maximum constraint violation is less than options.TolCon Active Constraints: 1 type pareto20 % Papageorgiou, 1996 % % x0 = 2 % goals: S* = [0.5 0.5]' % weights: w = [0.5 0.5]' % xo = 0.1429 % S(xo) = [1.0102 1.0102]' global e xo=[]; So=[]; F1=[]; F2=[]; for e=1:0.01:1.125 [x,S,ns,lambda]=sqp('test20','restr20',2); xo=[xo x]; So=[So S]; F1=[F1 1+0.5*x.^2]; F2=[F2 4*(x-0.5).^2+0.5]; end e=[1:0.01:1.125]; figure(3); plot(e,xo) edit pareto20 disp(sprintf('%d',feature('SessionTool'))) 0 ; dbstatus dbstack dbstack ; disp(which('pareto20')); V:\Cursos\Pos\Otimiza\Aulas\pareto20.m mdbstatus 'v:\cursos\pos\otimiza\aulas\pareto20.m' eval( 'if exist(''test20'',''var''), mauifunc(test20), end', ''); eval( 'if exist(''restr20'',''var''), mauifunc(restr20), end', ''); disp(which('pareto20')); V:\Cursos\Pos\Otimiza\Aulas\pareto20.m clear 'v:\cursos\pos\otimiza\aulas\pareto20.m' eval( 'if exist(''Papageorgiou'',''var''), mauifunc(Papageorgiou), end', ''); eval( 'if exist(''test20'',''var''), mauifunc(test20), end', ''); eval( 'if exist(''x'',''var''), mauifunc(x), end', ''); 0.4899 eval( 'if exist(''x'',''var''), mauifunc(x), end', ''); 0.4899 eval( 'if exist(''x'',''var''), mauifunc(x), end', ''); 0.4899 eval( 'if exist(''So'',''var''), mauifunc(So), end', ''); Columns 1 through 7 1.5000 1.0143 0.8600 0.7602 0.6886 0.6351 0.5944 Columns 8 through 13 0.5633 0.5400 0.5229 0.5111 0.5038 0.5004 eval( 'if exist(''x'',''var''), mauifunc(x), end', ''); 0.4899 eval( 'if exist(''S'',''var''), mauifunc(S), end', ''); 0.5004 eval( 'if exist(''Papageorgiou'',''var''), mauifunc(Papageorgiou), end', ''); disp(which('pareto20')); V:\Cursos\Pos\Otimiza\Aulas\pareto20.m clear 'v:\cursos\pos\otimiza\aulas\pareto20.m' ; pareto20 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 2 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 0.125 1 -2.22e-008 4 11 0.75 0.03125 1 0.375 5 14 1.16016 0.004395 1 0.152 6 17 1.32129 0.001099 1 0.085 7 20 1.40845 0.0002747 1 0.0447 8 23 1.45367 6.866e-005 1 0.0229 9 26 1.4767 1.717e-005 1 0.0116 10 29 1.48832 4.292e-006 1 0.00583 11 32 1.49415 1.073e-006 1 0.00292 12 35 1.49707 2.682e-007 1 0.00146 13 38 1.49854 6.706e-008 1 0.000732 Hessian modified 14 41 1.49927 1.676e-008 1 0.000366 Hessian modified 15 44 1.49963 4.192e-009 1 0.000183 Hessian modified 16 47 1.49982 1.048e-009 1 9.16e-005 Hessian modified 17 50 1.49991 2.62e-010 1 4.58e-005 Hessian modified 18 53 1.49995 6.551e-011 1 2.29e-005 Hessian modified 19 56 1.49998 1.641e-011 1 1.15e-005 Hessian modified 20 59 1.49999 4.102e-012 1 5.73e-006 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.99 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 0.115 1 -2.04e-008 4 11 0.7116 0.02645 1 0.269 5 14 0.990637 0.001216 1 0.0227 6 17 1.01365 3.296e-005 1 0.000667 7 20 1.01431 2.707e-008 1 5.49e-007 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.98 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 0.105 1 -1.87e-008 4 11 0.6764 0.02205 1 0.191 5 14 0.864514 -0.0003732 1 -0.00455 6 17 0.859979 1.774e-006 1 2.13e-005 Hessian modified 7 20 0.86 3.923e-011 1 4.71e-010 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.97 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 0.095 1 -1.69e-008 4 11 0.6444 0.01805 1 0.133 5 14 0.769201 -0.001061 1 -0.00916 6 17 0.760123 9.732e-006 1 8.1e-005 Hessian modified 7 20 0.760204 7.884e-010 1 6.57e-009 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.96 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 0.085 1 -1.51e-008 4 11 0.6156 0.01445 1 0.0908 5 14 0.696439 -0.001249 1 -0.00795 6 17 0.688567 1.006e-005 1 6.18e-005 Hessian modified 7 20 0.688629 6.324e-010 1 3.88e-009 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.95 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 0.075 1 -1.33e-008 4 11 0.59 0.01125 1 0.06 5 14 0.640625 -0.001172 1 -0.00562 Hessian modified twice 6 17 0.635056 7.031e-006 1 3.27e-005 Hessian modified 7 20 0.635089 2.47e-010 1 1.15e-009 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.94 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 0.065 1 -1.15e-008 4 11 0.5676 0.00845 1 0.038 5 14 0.597852 -0.0009717 1 -0.00354 Hessian modified twice 6 17 0.594345 3.999e-006 1 1.42e-005 Hessian modified 7 20 0.594359 6.642e-011 1 2.36e-010 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.93 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 0.055 1 -9.77e-009 4 11 0.5484 0.00605 1 0.0228 5 14 0.565325 -0.0007314 1 -0.00201 Hessian modified twice 6 17 0.563332 1.931e-006 1 5.19e-006 Hessian modified 7 20 0.563337 1.322e-011 1 3.56e-011 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.92 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 0.045 1 -7.99e-009 4 11 0.5324 0.00405 1 0.0126 5 14 0.541006 -0.0004992 1 -0.00101 Hessian modified twice 6 17 0.539998 7.837e-007 1 1.57e-006 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.91 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 0.035 1 -6.22e-009 4 11 0.5196 0.00245 1 0.00619 5 14 0.523377 -0.0003016 1 -0.000435 Hessian modified twice 6 17 0.522943 2.535e-007 1 3.62e-007 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.9 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 0.025 1 -4.44e-009 4 11 0.51 0.00125 1 0.0025 5 14 0.511289 -0.0001514 1 -0.000144 Hessian modified twice 6 17 0.511146 5.736e-008 1 5.42e-008 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.89 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 0.015 1 -2.66e-009 4 11 0.5036 0.00045 1 0.000686 5 14 0.503862 -5.3e-005 1 -2.81e-005 Hessian modified twice 6 17 0.503834 6.385e-009 1 3.37e-009 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.88 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 0.005 1 -8.88e-010 4 11 0.5004 5e-005 1 5.45e-005 5 14 0.500409 -5.675e-006 1 -9.37e-007 Hessian modified twice Optimization terminated successfully: Magnitude of directional derivative in search direction less than 2*options.TolFun and maximum constraint violation is less than options.TolCon Active Constraints: 1 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.87 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.005 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.86 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.015 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.85 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.025 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.84 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.035 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.83 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.045 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.82 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.055 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.81 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.065 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.8 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.075 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.79 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.085 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.78 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.095 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.77 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.105 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.76 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.115 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.75 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.125 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.74 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.135 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.73 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.145 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.72 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.155 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.71 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.165 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.7 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.175 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.69 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.185 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.68 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.195 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.67 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.205 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.66 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.215 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.65 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.225 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.64 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.235 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.63 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.245 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.62 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.255 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.61 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.265 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.6 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.275 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.59 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.285 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.58 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.295 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.57 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.305 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.56 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.315 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.55 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.325 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.54 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.335 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.53 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.345 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.52 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.355 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.51 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.365 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.5 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.375 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.49 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.385 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.48 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.395 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.47 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.405 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.46 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.415 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.45 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.425 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.44 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.435 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.43 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.445 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.42 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.455 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.41 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.465 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.4 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.475 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.39 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.485 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.38 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.495 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.37 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.5 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.36 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.5 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.35 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.5 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.34 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.5 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.33 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.5 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.32 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.5 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.31 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.5 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.3 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.5 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.29 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.5 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.28 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.5 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.27 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.5 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.26 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.5 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.25 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.5 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.24 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.5 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.23 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.5 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.22 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.5 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.21 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.5 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.2 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.5 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.19 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.5 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.18 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.5 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.17 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.5 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.16 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.5 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.15 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.5 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.14 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.5 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.13 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.5 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.12 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.5 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.11 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.5 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.1 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.5 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.09 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.5 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.08 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.5 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.07 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.5 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.06 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.5 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.05 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.5 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.04 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.5 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.03 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.5 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.02 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.5 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1.01 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.5 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 2 9.5 1 1 -24 2 5 1.5 1.215e-008 1 -2 3 8 0.5 -0.5 1 -9.86e-016 Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon No Active Constraints plot(F1,F2) figure(3); plot(e,xo) what M-files in the current directory V:\Cursos\Pos\Otimiza\Aulas CATALIS gmilp1 htest4 restr24eq EXTRATOR gminlp1 htest9 rosembr LUCRO gminlp2 interior set1 MINQUA gminlp3 karmarkar setoptim MODELO gminlp4 lmarqua sol_extrat Minqua44 gminlp5 lp_nlp sqp Modelo44 gminlp6 milp steepdes OPT_RES gmodelagem milp1 swarm ObjFunSa gmurray milprog test0 PLANOS grad minlp test1 READ2 grestr1 minlp1 test10 SEMIDEF grestr14 minlp2 test11 SMODELO grestr14eq minlp3 test12 ShowData grestr15 minlp4 test13 aurea grestr16 minlp5 test14 bandem1 grestr17 minlp6 test15 bfgs grestr20 minlpn test16 bracket grestr21 modelagem test17 buscarnd grestr23 naturais test18 cgrad grestr24 newton test19 checkbounds grestr24eq newton_h test1gn coggins grg newton_mod test1m compdir grg_ml newtont test2 complex gtest1 nlconst test20 dados_ex6_44 gtest10 nlp_internal test21 dfp gtest12 pareto18 test22 dual gtest13 pareto19 test23 ex2_karm gtest14 pareto20 test24 ex_karma gtest14eq pareto21 test3 ex_qp1 gtest16 powell test4 ex_qp2 gtest17 qpsub test5 ex_qp3 gtest2 refino test6 ex_swarm gtest20 restr test7 exmilp gtest21 restr1 test8 exmilp2 gtest23 restr14 test9 exmilprog gtest24 restr14eq teste_buscarnd exmilprog2 gtest24eq restr15 univar extrat gtest8 restr16 varmetr fmincon1 gtest9 restr17 visual fminunc1 hkjeeves restr20 writearq fminusub htest1 restr21 xplot fun htest10 restr23 func44 htest2 restr24 type pareto21 % Papageorgiou, 1996 % % x0 = 2 % goals: S* = [0.5 0.5]' % weights: w = [0.5 0.5]' % xo = 0.1429 % S(xo) = [1.0102 1.0102]' global w xo=[]; So=[]; F1=[]; F2=[]; for w=0:0.1:1 [x,S,ns,lambda]=sqp('test21','restr21',[2 0]); xo=[xo x]; So=[So S]; F1=[F1 1+0.5*x(1).^2]; F2=[F2 4*(x(1)-0.5).^2+0.5]; end w=[0:0.1:1]; type test21 function S=test(x) % Papageorgiou, 1996 % % x0 = 2 % goals: S* = [0.5 0.5]' % weights: w = [0.5 0.5]' % xo = 0.1429 % S(xo) = [1.0102 1.0102]' S=x(2); % [x,S,ns,lambda]=sqp('test21','restr21',[2 0]) type restr21 function [g,h]=restr(x) % Papageorgiou, 1996 % % x0 = 2 % goals: S* = [0.5 0.5]' % weights: w = [0.5 0.5]' % xo = 0.1429 % S(xo) = [1.0102 1.0102]' F1s=0.5; F2s=0.5; global w w1=w; w2=1-w; g(1,:)=1+0.5*x(1).^2-w1*x(2)-F1s; g(2,:)=4*(x(1)-0.5).^2+0.5-w2*x(2)-F2s; g(3,:)=-x(1); h=[]; % [x,S,ns,lambda]=sqp('test21','restr21',[2 0]) type test21 function S=test(x) % Papageorgiou, 1996 % % x0 = 2 % goals: S* = [0.5 0.5]' % weights: w = [0.5 0.5]' % xo = 0.1429 % S(xo) = [1.0102 1.0102]' S=x(2); % [x,S,ns,lambda]=sqp('test21','restr21',[2 0]) global w w=0.5 w = 0.5000 [x,S,ns,lambda]=sqp('test21','restr21',[2 0]) max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 3 0 9 1 -0.647 2 7 -0.647059 0.9965 1 1.3 3 11 0.653979 0.673 1 0.346 4 15 1 0.0625 1 0.02 5 19 1.02 0.001225 1 0.000408 Hessian modified 6 23 1.02041 5.097e-007 1 1.7e-007 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 2 x = 0.1429 1.0204 S = 1.0204 ns = 25 lambda = lower: [2x1 double] upper: [2x1 double] eqlin: [0x1 double] eqnonlin: [0x1 double] ineqlin: [0x1 double] ineqnonlin: [3x1 double] type pareto21 % Papageorgiou, 1996 % % x0 = 2 % goals: S* = [0.5 0.5]' % weights: w = [0.5 0.5]' % xo = 0.1429 % S(xo) = [1.0102 1.0102]' global w xo=[]; So=[]; F1=[]; F2=[]; for w=0:0.1:1 [x,S,ns,lambda]=sqp('test21','restr21',[2 0]); xo=[xo x]; So=[So S]; F1=[F1 1+0.5*x(1).^2]; F2=[F2 4*(x(1)-0.5).^2+0.5]; end w=[0:0.1:1]; pareto21 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 3 0 9 1 -1 2 7 -1 1.25 1 0 infeasible Optimization terminated: No feasible solution found. Magnitude of directional derivative in search direction less than 2*options.TolFun but constraints are not satisfied. max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 3 0 9 1 -0.935 2 7 -0.935162 1.007 1 3.46 3 11 2.52725 0.2473 1 2.47 4 15 5 0 1 -1.07e-007 Hessian modified twice Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 3 0 9 1 -0.866 2 7 -0.866337 0.8933 1 2.27 3 11 1.39986 0.22 1 1.1 4 15 2.5 0 1 -3.66e-008 Hessian modified twice Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 3 0 9 1 -0.795 2 7 -0.794621 0.9373 1 1.8 3 11 1.00347 0.2976 1 0.663 4 15 1.66667 3.309e-024 1 -8.27e-009 Hessian modified twice Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 3 0 9 1 -0.721 2 7 -0.721154 0.9719 1 1.51 3 11 0.791305 0.5252 1 0.459 4 15 1.25 0.01563 1 0.00543 5 19 1.25543 4.992e-005 1 1.75e-005 Hessian modified 6 23 1.25545 5.143e-010 1 1.8e-010 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 2 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 3 0 9 1 -0.647 2 7 -0.647059 0.9965 1 1.3 3 11 0.653979 0.673 1 0.346 4 15 1 0.0625 1 0.02 5 19 1.02 0.001225 1 0.000408 Hessian modified 6 23 1.02041 5.097e-007 1 1.7e-007 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 2 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 3 0 9 1 -0.573 2 7 -0.573394 1.011 1 1.13 3 11 0.554948 0.778 1 0.278 4 15 0.833333 0.1111 1 0.0333 5 19 0.866667 0.005378 1 0.00179 6 23 0.868453 1.544e-005 1 5.16e-006 Hessian modified 7 27 0.868458 1.169e-010 1 3.91e-011 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 2 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 3 0 9 1 -0.501 2 7 -0.501114 1.016 1 0.98 3 11 0.478445 0.8565 1 0.236 4 15 0.714286 0.1543 1 0.0439 5 19 0.758158 0.01352 1 0.00466 6 23 0.762816 0.0001524 1 5.37e-005 Hessian modified 7 27 0.76287 1.997e-008 1 7.04e-009 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 2 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 3 0 9 1 -0.431 2 7 -0.431034 1.012 1 0.848 3 11 0.416496 0.9167 1 0.209 4 15 0.625 0.1914 1 0.0519 5 19 0.676907 0.02589 1 0.00963 6 23 0.686533 0.0008904 1 0.000355 Hessian modified 7 27 0.686888 1.216e-006 1 4.87e-007 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 2 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 3 0 9 1 -0.364 2 7 -0.363825 0.9993 1 0.728 3 11 0.364599 0.9635 1 0.191 4 15 0.555556 0.223 1 0.058 5 19 0.613518 0.04234 1 0.0177 6 23 0.631261 0.003967 1 0.00205 7 27 0.633307 5.276e-005 1 2.8e-005 Hessian modified 8 31 0.633335 9.917e-009 1 5.26e-009 Hessian modified Optimization terminated successfully: Search direction less than 2*options.TolX and maximum constraint violation is less than options.TolCon Active Constraints: 1 2 max Directional Iter F-count f(x) constraint Step-size derivative Procedure 1 3 0 9 1 -0.3 2 7 -0.3 0.98 1 0.62 3 11 0.32 1 1 0.18 4 15 0.5 0.25 1 0.0625 5 19 0.5625 0.0625 1 0.0313 6 23 0.593756 0.01562 1 0.0156 7 27 0.609378 0.003905 1 0.00781 8 31 0.617189 0.0009762 1 0.00391 9 35 0.621094 0.0002441 1 0.00195 10 39 0.623047 6.101e-005 1 0.000976 11 43 0.624024 1.525e-005 1 0.000488 Hessian modified 12 47 0.624512 3.814e-006 1 0.000244 Hessian modified 13 51 0.624756 9.534e-007 1 0.000122 Hessian modified 14 55 0.624878 2.384e-007 1 6.1e-005 Hessian modified 15 59 0.624939 5.961e-008 1 3.05e-005 Hessian modified 16 63 0.624969 1.491e-008 1 1.53e-005 Hessian modified 17 67 0.624985 3.731e-009 1 7.63e-006 Hessian modified 18 71 0.624992 9.347e-010 1 3.81e-006 Hessian modified 19 75 0.624996 2.346e-010 1 1.91e-006 Hessian modified Optimization terminated successfully: Magnitude of directional derivative in search direction less than 2*options.TolFun and maximum constraint violation is less than options.TolCon Active Constraints: 1 2 plot(F1,F2) quit