最优化方法——外点罚函数法

function [A,B]=Exterior(f,p,eps)
format long;
d=1;
e1=1e-4;
k=1;
A(k)=0;B(k)=0;
r(k)=1;a=2;
while d>eps
    x1=A(k);x2=B(k);
    if vpa(p(x1,x2))>0
        u1=1;
    else
        u1=0;
    end
    F=f+r(k)*u1*p^2;
    Fx1=diff(F,'x1');
    Fx2=diff(F,'x2');
    Fx11=diff(Fx1,'x1');
    Fx12=diff(Fx1,'x2');
    Fx21=diff(Fx2,'x1');
    Fx22=diff(Fx2,'x2');
    for n=1:100
        F1=subs(Fx1); %求解梯度值和海森矩阵
        F2=subs(Fx2);
        F11=subs(Fx11);
        F12=subs(Fx12);
        F21=subs(Fx21);
        F22=subs(Fx22);
        if(double(sqrt(F1^2+F2^2))<=e1) %梯度法最优值收敛条件
            A(k+1)=double(x1);B(k+1)=double(x2);
            break;
        else
            X=[x1 x2]'-([F11 F12;F21 F22])\[F1 F2]';
            x1=X(1,1);x2=X(2,1);
        end
    end
    d=norm((A(k+1)-A(k)),(B(k+1)-B(k)));
    r(k+1)=a*r(k);
    k=k+1;
end
A(k)
B(k)
double(subs(f))

clear all;
clc
syms x1 x2 x;
gama=1.1;
f=x1^2+(1/3)*x2^2;
p=x1+x2-1;
eps=1e-4;
[A,B]=Exterior(f,p,eps)

function f=myfun(x)
f=x(1)^2+(1/3)*x(2)^2;

function p=myfun2(Aeq,beq,x)
p=Aeq*[x(1);x(2)]-beq;