um.m

非常经典的最优化程序

%DFP计算算法(精确一维搜索,k=16,mul_count=9048,sum_count=4251花费时间很少)
syms x1 x2 ar;
f=x1^2-x1*x2+x2^2+2*x1-4*x2;
v=[x1,x2];
df=jacobian(f,v);
df=df.';
epson=1e-12;x0=[2,2]';g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)});k=0;H0=[1,0;0,1];mul_count=0;sum_count=0;
mul_count=mul_count+7;sum_count=sum_count+4;
while(norm(g1)>epson&k<=2)
     mul_count=mul_count+2;sum_count=sum_count+1;
    if k==0
         p=-H0*g1;mul_count=mul_count+7;sum_count=sum_count+4;
    else
        H1=H0-H0*yk*yk'*H0/(yk'*H0*yk)+sk*sk'/(yk'*sk);mul_count=mul_count+36;sum_count=sum_count+18;
        p=-H1*g1;mul_count=mul_count+7;sum_count=sum_count+4;
        H0=H1;
    end
    x00=x0;
    y=subs(f,{x1,x2},{x0(1,1)+ar*p(1,1),x0(2,1)+ar*p(2,1)});mul_count=mul_count+18;sum_count=sum_count+12;
    result1=qujian(y,ar);
    b1=result1(1);mul_count=mul_count+result1(2);sum_count=sum_count+result1(3);
    result2=Asearch(y,ar,b1);
    arf=result2(1);mul_count=mul_count+result2(2);sum_count=sum_count+result2(3);
    x0=x0+arf*p;
    g0=g1;
    g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)});
    p0=p;
    yk=g1-g0; sk=x0-x00;
    k=k+1;
    mul_count=mul_count+9;sum_count=sum_count+11;
end;
k
x0
mul_count
sum_count