1、用惩罚函数外点法求解以下约束最优化问题程序用惩罚函数外点法求解以下约束最优化问题：，当惩罚因子分别为5，10，50，100的计算结果。解：构造外点法惩罚函数x，r=x1+x2+rmax(0,x12-x2)2+rmax(0,-x1)2 =x1+x2 (g1(x)0,g2(x)0)x1+x2+r(x12-x2)2+r(-x1)2 (g1(x)0,g2(x)0)对上式求偏导得x1=11+4r*x1*x12-x2+2rx1x2=11-2r(x12-x2)无约束目标函数极小化问题的最优解系列为：x1*r=-12+2rx2*r=14(1+r)2-12r惩罚函数外点法的M文件：syms x1 x2f=x1+
2、x2;g1=x12-x2;g2=-x1;r0=5;c=0.5;km=7;k=1:km;r=r0*c.(k-1);x1=-1./(2+2.*r);x2=1./(4.*(1+r).2)-1./2.*r;g1=x1.2-x2;g2=-x1;f=x1+x2;p=x1+x2+r.*g1.2+r.*g2.2;krx1x2p当r=5时的运行结果如下：k = 1 2 3 4 5 6 7r = 5.0000 2.5000 1.2500 0.6250 0.3125 0.1563 0.0781x1 = -0.0833 -0.1429 -0.2222 -0.3077 -0.3810 -0.4324 -0.4638x2
3、 = -2.4931 -1.2296 -0.5756 -0.2178 -0.0111 0.1089 0.1760p = 28.7083 2.5848 -0.2478 -0.4053 -0.3391 -0.2934 -0.2708当r=10时的运行结果如下：k = 1 2 3 4 5 6 7r = 10.0000 5.0000 2.5000 1.2500 0.6250 0.3125 0.1563x1 = -0.0455 -0.0833 -0.1429 -0.2222 -0.3077 -0.3810 -0.4324x2 = -4.9979 -2.4931 -1.2296 -0.5756 -0.21
4、78 -0.0111 0.1089p = 244.9773 28.7083 2.5848 -0.2478 -0.4053 -0.3391 -0.2934当r=50时的运行结果如下：k = 1 2 3 4 5 6 7r = 50.0000 25.0000 12.5000 6.2500 3.1250 1.5625 0.7813x1 = -0.0098 -0.0192 -0.0370 -0.0690 -0.1212 -0.1951 -0.2807x2 = -24.9999 -12.4996 -6.2486 -3.1202 -1.5478 -0.7432 -0.3118p = 1.0e+04 * 3.
5、1225 0.3894 0.0482 0.0058 0.0006 0.0000 -0.0000当r=100时的运行结果如下：k = 1 2 3 4 5 6 7r = 100.0000 50.0000 25.0000 12.5000 6.2500 3.1250 1.5625x1 = -0.0050 -0.0098 -0.0192 -0.0370 -0.0690 -0.1212 -0.1951x2 = -50.0000 -24.9999 -12.4996 -6.2486 -3.1202 -1.5478 -0.7432p = 1.0e+05 * 2.4995 0.3122 0.0389 0.0048 0.0006 0.0001 0.0000
