qmin.m

function [s,phis,ds,dphi,S]=qmin(phi,a,b,delta,epsilon)
%输入: phi 是目标函数, a和b是搜索区间的端点
% delta,epsilon是容许误差
%输出: s是近似极小点, phis是对应的近似极小值; k是迭代次数
% ds是迭代终止时的步长, dphi是|phi(s1)-phi(s)|; S是迭代向量
s0=a; maxj=20; maxk=30; big=1e6; err=1; k=1;
S(k)=s0; cond=0;  h=1; ds=0.00001;
if 
    (abs(s0)>1e4), h=abs(s0)*(1e-4); 
end
while 
    (k<maxk & err>epsilon &cond~=5)
    f1=(feval(phi,s0+ds)-feval(phi,s0-ds))/(2*ds);
    if
        (f1>0), h=-abs(h); 
    end
    s1=s0+h;     
    s2=s0+2*h;      
    bars=s0;
    phi0=feval(phi,s0);  
    phi1=feval(phi,s1);
    phi2=feval(phi,s2);  
    barphi=phi0; 
    cond=0;
    j=0; %确定h使得phi1?phi0且phi1?phi2 while(j?maxj&abs(h)?delta&cond==0)
        if (phi0<=phi1),
            s2=s1; phi2=phi1; h=0.5*h;
            s1=s0+h; phi1=feval(phi,s1);
        else if (phi2<phi1),
                s1=s2; phi1=phi2; h=2*h;
                s2=s0+2*h; phi2=feval(phi,s2);
            else
                
                cond=-1; 
            end
        end
        j=j+1;
        if
            (abs(h)>big|abs(s0)>big), cond=5; 
        end
end
if(cond==5)
    bars=s1; 
    barphi=feval(phi,s1);
else
%二次插值求phis 
            d=2*(2*phi1-phi0-phi2); 
            if(d<0),
            barh=h*(4*phi1-3*phi0-phi2)/d;
        else
            barh=h/3; cond=4;
        end
        bars=s0+barh;   
        barphi=feval(phi,bars);
        h=abs(h);  
        h0=abs(barh);
        h1=abs(barh-h);  
        h2=abs(barh-2*h);
%确定下一次迭代的h值
     if(h0<h), h=h0;end
     if(h1<h), h=h1;end
     if(h2<h), h=h2;end
     if(h==0), h=barh;end
     if(h<delta), cond=1;end 
     if(abs(h)>big|abs(bars)>big), cond=5; end 
     err=abs(phi1-barphi);
     s0=bars;  k=k+1; S(k)=s0;
end
    if(cond==2&h<delta), cond=3; end
end
s=s0;  phis=feval(phi,s);
ds=h;  dphi=err;