最速下降法.txt

约束最优化方法－－最速下降法(也叫梯度法)

syms x1 x2  g G gk Gk xk xk2 i sk ak ak2 amin fk fk2 gf gfk Gf Gfk ai ai2 e temp gk2 Gk2 gk3 Gk3
f=(x1+10*x2)^2+5*(x3-x4)^2+(x2-2*x3)^4+10*(x1-x4)^4;
g=jacobian(f);
xk=[3,-1];
xk2=xk;
i=0;
n=2;
while(n>1)
    i=i+1
    x1=xk(1);x2=xk(2);
    gk=subs(g);
    sk=-gk;
    
    
    xk2=xk2+ak*sk;
    x1=xk2(1);x2=xk2(2);
    f=(x1+10*x2)^2+5*(x3-x4)^2+(x2-2*x3)^4+10*(x1-x4)^4;
    fk=subs(f);
    fk=inline(fk);
    [amin]=fminsearch(fk,0);   
    
    xk=xk+amin*sk
    xk2=xk;
    n=norm(gk,2)
    ak=ak2;
    
end