有效集 matlab代码

%有效集
function activeset
H=[2 -1; -1 4];
c=[-1 -10]';
Ae=[ ]; be=[ ];
Ai=[-3 -2; 1 0; 0 1];
bi=[-6 0 0]';
x0=[0 0]';
[x,lambda,exitflag,output]=qpact(H,c,Ae,be,Ai,bi,x0)

function [x,lamk,exitflag,output]=qpact(H,c,Ae,be,Ai,bi,x0) 

% 初始化
epsilon=1.0e-9; err=1.0e-6;
k=0; x=x0;
n=length(x); kmax=1.0e3;
ne=length(be); ni=length(bi);
lamk=zeros(ne+ni,1);
index=ones(ni,1);
for i=1:ni
    if (Ai(i,:)*x>bi(i)+epsilon)
        index(i)=0;
    end
end
while (k<=kmax)
    %求解子问题
    Aee=[]; if(ne>0), Aee=Ae; end
    for j=1:ni
        if(index(j)>0), Aee=[Aee; Ai(j,:)]; end
    end
    gk=H*x+c;
    [m1,n1] = size(Aee);
    [dk,lamk]=qsubp(H,gk,Aee,zeros(m1,1));
    if(norm(dk)<=err)
        y=0.0;
        if(length(lamk)>ne)
            [y,jk]=min(lamk(ne+1:length(lamk))); end
        if(y>=0)
            exitflag=0;
        else
            exitflag=1;
            for i=1:ni
                if(index(i)&&(ne+sum(index(1:i)))==jk)
                    index(i)=0;
                    break;
                end
            end
        end
        k=k+1;
    else
        exitflag=1;
        %求步长
        alpha=1.0; tm=1.0;
        for i=1:ni
            if((index(i)==0)&&(Ai(i,:)*dk<0))
                tm1=(bi(i)-Ai(i,:)*x)/(Ai(i,:)*dk);
                if(tm1<tm)
                    tm=tm1; ti=i;
                end
            end
        end
        alpha=min(alpha,tm);
        x=x+alpha*dk;
        %修正有效集
        if(tm<1), index(ti)=1;
        end
    end
    if(exitflag==0), break; end
    k=k+1;
end
output.fval=0.5*x'*H*x+c'*x;
output.iter=k;

% 求解子问题
function [x,lambda]=qsubp(H,c,Ae,be)
ginvH=pinv(H);
[m,n]=size(Ae);
if(m>0)
    rb=Ae*ginvH*c + be;
    lambda=pinv(Ae*ginvH*Ae')*rb;
    x=ginvH*(Ae'*lambda-c);
else
    x=-ginvH*c;
    lambda=0;
end