变尺度.txt

约束最优化方法－－最速下降法(也叫梯度法)

syms x1 x2 gk gk2 Gk sk sk2 ak xk xk1 xk2 n i amin zhi
f=x1^2+x2^2+x1*x2;       %%原函数
g=jacobian(f); %%梯度
x1=3;x2=-1;
xk=[3,-1]';
n=2;
i=0;
gk=subs(g);
gk=gk';
xk2=xk;
Hk=[1,0;0,1];
sk=(-Hk)*gk;
while(n>0.001)
    i=i+1
    gk2=gk;
    temp=xk;
    %%%%%%%%%%%%%%%%%%%%%%%%%%线性搜索步长因子
    xk2=xk2+ak*sk;
    x1=xk2(1);x2=xk2(2);
    fk=subs(f);
    fk=inline(fk);
    [amin]=fminsearch(fk,0);
    %%%%%%%%%%%%%%%%%%%%%%%%%求出X(k+1)
    xk=xk+amin*sk;
    xk2=xk;
    x1=xk(1);x2=xk(2);
    gk=subs(g);
    gk=gk';
    
    
    %%求下降方向
    dk=xk-temp;
    rk=gk-gk2;
    Hk=Hk+(1+(rk'*Hk*rk)/(dk'*rk))*((dk*dk')/(dk'*rk))-(dk*rk'*Hk+Hk*rk*dk')/(dk'*rk);
    sk=-Hk*gk;
    %%Input out the MinPoin and the Norm 
    n=norm(gk,2);
    Xk=xk
end