usearch1.m

非常经典的最优化程序

%不精确一维搜索法
function result=Usearch1(f,x1,x2,df,x0,p)
mu=0.001;sgma=0.99;a=0;b=inf;arf=1;m_count=0;s_count=0;
pk=p;
x3=x0;
x4=x3+arf*pk;m_count=m_count+2;s_count=s_count+2;
f1=subs(f,{x1,x2},{x3(1,1),x3(2,1)});m_count=m_count+4;s_count=s_count+3;
f2=subs(f,{x1,x2},{x4(1,1),x4(2,1)});m_count=m_count+4;s_count=s_count+3;
gk1=subs(df,{x1,x2},{x3(1,1),x3(2,1)});m_count=m_count+7;s_count=s_count+4;
gk2=subs(df,{x1,x2},{x4(1,1),x4(2,1)});m_count=m_count+7;s_count=s_count+4;
while (f1-f2<=-mu*arf*gk1'*pk)
   b=arf;arf=(a+arf)/2;x4=x3+arf*pk;f2=subs(f,{x1,x2},{x4(1,1),x4(2,1)});gk2=subs(df,{x1,x2},{x4(1,1),x4(2,1)});
   m_count=m_count+19;s_count=s_count+12;
end;
m_count=m_count+5;s_count=s_count+2;
while (1>0)
    if(gk2'*pk<sgma*gk1'*pk)
        a=arf;a=min(2*arf,(a+b)/2);x4=x3+arf*pk;f2=subs(f,{x1,x2},{x4(1,1),x4(2,1)});gk2=subs(df,{x1,x2},{x4(1,1),x4(2,1)});
        m_count=m_count+21;s_count=s_count+12;
    while (f1-f2<=-mu*arf*gk1'*pk)
        b=arf;arf=(a+arf)/2;x4=x3+arf*pk;f2=subs(f,{x1,x2},{x4(1,1),x4(2,1)});gk2=subs(df,{x1,x2},{x4(1,1),x4(2,1)});
        m_count=m_count+19;s_count=s_count+12;
    end;
    m_count=m_count+5;s_count=s_count+2;
    else 
        break;
    end
end;
result=[arf,m_count,s_count];