最优化作业 共轭梯度法 matlab代码

Posted 2020-11-04 夜游星

syms f x1 x2 
f=(1/2)*x1^2+x2^2;
x=[2;1];
a=[1 0;0 2];% A
g1=diff(f,x1);
g2=diff(f,x2);
g=[g1;g2];%导数

%            x1
g11=subs(g1,{x1,x2},{x(1) x(2)});
g22=subs(g2,{x1,x2},{x(1) x(2)});
g=[g11;g22]
d=-g;
d11=subs(d(1),{x1,x2},{x(1) x(2)});
d22=subs(d(2),{x1,x2},{x(1) x(2)});
d=[d11;d22]
af=(-g‘*d)/(d‘*a*d)
x=x+af*d
g11=subs(g1,{x1,x2},{x(1) x(2)});
g22=subs(g2,{x1,x2},{x(1) x(2)});
g=[g11;g22]
%             x1

e=0.1;%精度
%共轭梯度
for i=1:2
    if g==0
        disp(‘x‘)
        x
        break
    else
        
   
        b=(g‘*a*d)/(d‘*a*d)%β
        d=-g+b*d;
        
        d11=subs(d(1),{x1,x2},{x(1) x(2)});
        d22=subs(d(2),{x1,x2},{x(1) x(2)});
        d=[d11;d22]
        
        af=(-g‘*d)/(d‘*a*d)%步长α
        
        x=x+af*d
        
        g11=subs(g1,{x1,x2},{x(1) x(2)});
        g22=subs(g2,{x1,x2},{x(1) x(2)});
        g=[g11;g22]
    end
end