无约束优化算法：单纯形法

单纯形法1. 算法原理单纯形法的基本思想是：设 是 中的 个点，构成一个当前的单纯形， 定义如下：(0)1(),.,nxR1maxin,(0)(1)()max),.nffxff()()()in( x记 为这个单纯形除去 外的所有顶点的形心，xmax()max01nii取 关于 的反射点 ， 构成新的单纯形，反复上述过程，直max(1)nx()ax()到达到停止条件。2. 函数 ifsearch1） 函数语法 in(,0)xffuxm,i(.)in.,mi(.)searchoptisfvlfxtgfearchflifutfs函数输入：目标函数fun：迭代初始点0x：函数参数设置optis函数输出：最优点：最优点对应的函数值fval：函数停止信息exitg1：函数收敛正常停止0：迭代次数，目标函数计算次数达到最大数-1：算法被输出函数停止：函数运算信息outp2） 函数使用（1 ） 目标函数程序 .BanFum()functiofx不 含 导 数 解 析 式0*(2)12(1)2x函数不需要导数信息。NeldrMaSiplex（2 ） 算法参数设置： .mUnc(rg, ,250,)optinstiLalofgrdbjofMaxFunEvlsdiplayiter（3 ） 函数调用运算： .Siplexc(ar,)tistlfrjxvlsilyiter1.9,2x,min(,)fvaleitfgoutpfsearchBnFuoptins3） 计算结果Iteration Func-count min f(x) Procedure0 1 267.62 1 3 236.42 initial simplex2 5 67.2672 expand3 7 12.2776 expand4 8 12.2776 reflect5 10 12.2776 contract inside6 12 6.76772 contract inside7 13 6.76772 reflect8 15 6.76772 contract inside9 17 6.76772 contract outside10 19 6.62983 contract inside11 21 6.55249 contract inside12 23 6.46084 contract inside13 24 6.46084 reflect14 26 6.46084 contract inside15 28 6.45544 contract outside16 30 6.42801 expand17 32 6.40994 expand18 34 6.32449 expand19 36 6.28548 expand20 38 6.00458 expand21 39 6.00458 reflect22 41 5.43287 expand23 42 5.43287 reflect24 44 4.63434 expand25 45 4.63434 reflect26 47 4.63434 contract inside27 49 4.63434 contract outside28 51 4.31027 expand29 53 4.31027 contract inside30 55 4.00991 expand31 56 4.00991 reflect32 58 3.55664 expand33 59 3.55664 reflect34 61 3.23438 reflect35 63 3.23438 contract inside36 65 2.9515 expand37 67 2.82878 reflect38 69 2.56426 reflect39 71 2.54453 contract outside40 73 2.43615 reflect41 75 2.34358 reflect42 77 2.28129 reflect43 79 2.21473 reflect44 81 2.08627 reflect45 82 2.08627 reflect46 84 1.86677 reflect47 86 1.86677 contract inside48 88 1.80424 reflect49 90 1.58432 expand50 91 1.58432 reflect51 93 1.27128 expand52 94 1.27128 reflect53 96 1.05673 reflect54 98 1.05673 contract inside55 100 0.816708 expand56 102 0.816708 contract inside57 104 0.816708 contract inside58 106 0.760575 reflect59 108 0.601009 expand60 110 0.601009 contract inside61 112 0.516477 reflect62 114 0.516477 contract inside63 115 0.516477 reflect64 117 0.416316 expand65 119 0.416316 contract inside66 120 0.416316 reflect67 122 0.345716 reflect68 124 0.345716 contract inside69 126 0.285909 expand70 128 0.281068 reflect71 130 0.22878 reflect72 132 0.22878 contract inside73 134 0.203104 expand74 136 0.148 expand75 138 0.0999997 expand76 140 0.0999997 contract inside77 141 0.0999997 reflect78 143 0.0217142 expand79 145 0.0217142 contract inside80 147 0.0217142 contract inside81 148 0.0217142 reflect82 150 0.0217142 contract inside83 152 0.0217142 contract inside84 154 0.0191193 reflect85 156 0.00610404 expand86 158 0.00610404 contract outside87 160 0.00261955 reflect88 161 0.00261955 reflect89 163 0.000256151 reflect90 165 0.000256151 contract inside91 166 0.000256151 reflect92 168 0.000256151 contract inside93 170 0.00020711 contract inside94 172 0.00010357 contract inside95 174 2.09236e-005 contract inside96 176 2.09236e-005 contract inside97 178 1.80497e-006 reflect98 180 1.80497e-006 contract inside99 182 1.80497e-006 contract inside100 184 1.80497e-006 contract inside101 185 1.80497e-006 reflect102 187 3.74217e-007 contract inside103 189 3.74217e-007 contract inside104 191 3.26526e-007 contract inside105 193 8.07652e-008 contract inside106 195 1.66554e-008 contract inside107 197 1.66554e-008 contract inside108 199 1.66554e-008 contract inside109 201 5.57089e-009 contract outside110 203 1.86825e-009 contract inside111 205 1.86825e-009 contract outside112 207 5.53435e-010 contract inside113 208 5.53435e-010 reflect114 210 4.06855e-010 contract insideOptimization terminated:the current x satisfies the termination criteria using OPTIONS.TolX of 1.000000e-004 and F(X) satisfies the con