http://www.elecfans.com/article/lab/matlab/2008/2008101714377.html
matlab最优化实验
6.1知识要点与背景
6.1.1 由简入繁: 最佳水槽断面问题的推广

6.1.2 微分法求最大和最小
◆问题4 (1)求受检点: ,
zxy6_1.m
【 syms x1 x2 %定义符号变量.
f=x1^3-x2^3+3*x1^2+3*x2^2-9*x1; % 函数z.
v=[x1 x2];df=jacobian(f,v) %计算雅可比 .
[X,Y]=solve(df(1),df(2));[X,Y] % 用指令solve求驻点. 】

zxy6_2.m
【 clf,xmin=-5;xmax=3.5;ymin=-3;ymax=5;
x1=linspace(xmin,xmax,30);x2=linspace(ymin,ymax,30);
[X1,X2]=meshgrid(x1,x2);Z= X1.^3.-X2.^3+3*X1.^2+3*X2.^2-9*X1;
contour(X1,X2,Z,60);,hold on, xp=[-3,1,-3,1];yp=[0 0 2 2];
plot(xp,yp,'ro'),axis([xmin xmax ymin ymax]),colorbar
xlabel('x_1'),ylabel('x_2'),
for i=1:length(xp)
text(xp(i),yp(i),['\leftarrow (',num2str(xp(i)),',',num2str(yp(i)),')'] )
end 】

6.2 实验与观察(Ⅰ):模拟盲人下山的迭代寻优法
zxy6_3.m(盲人下山的模拟)
【 clf, a=-2;b=4;
xmin=a;xmax=b;ymin=a;ymax=b; %设置变量范围和坐标轴显示范围.
x1=linspace(xmin,xmax,100);x2=linspace(ymin,ymax,100);
[X1,X2]=meshgrid(x1,x2);
[Z,DZ1,DZ2]=zxy6_3f(X1,X2); %计算函数和梯度向量.
contour(X1,X2,Z,30), %画等值线图.
axis([xmin xmax ymin ymax]),hold on,
axis equal, %该命令将使横轴,纵轴具有相同比例,避免失真.
plot([1.46808510638298],[1.148936170212776],'o'), %标注最优点.
axis([xmin xmax ymin ymax])
x=[];y=[]; %开始用鼠标选点,按左键选点,按右键中止选点过程.
disp('Select a point by put on mouse left-key')
%disp指令,在命令窗口显示文字.
disp('Stop selecting point by put on mouse right-key')
button=1; %button和ginput命令结合使用可用鼠标选点, 按左键时button=1.

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