prp1.m

非常经典的最优化程序

%PRP直接计算降法(精确一维搜索,k=19,mul_count=8390,sum_count=3745,花费时间很少)
syms x1 x2 ar;
f=50*(x2-x1^2)^2+(1-x1)^2;
v=[x1,x2];
df=jacobian(f,v);
df=df.';
epson=1e-12;x0=[0,0]';g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)});k=0;mul_count=0;sum_count=0;
mul_count=mul_count+7;sum_count=sum_count+4;
while(norm(g1)>epson)
    mul_count=mul_count+2;sum_count=sum_count+1;
    if k==0
         p=-g1;
    else
        bta=(g1'*(g1-g0))/(g0'*g0); 
        p=-g1+bta*p0;
        mul_count=mul_count+7;sum_count=sum_count+6;
    end
    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;
    k=k+1;
    mul_count=mul_count+9;sum_count=sum_count+7;
end;
k
x0
mul_count
sum_count