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QPhild.m
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QPhild.m
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function eta = QPhild(H,f,A_cons,b)
% E=H;
% F=f;
% M=A_cons;
% gamma=b;
% eta = x
[n1,m1]=size(A_cons);
eta = -H\f;
kk = 0;
for i = 1:n1
if (A_cons(i,:)*eta>b(i))
kk = kk+1;
else
kk = kk+0;
end
end
if (kk == 0)
return;
end
P = A_cons*(H\A_cons');
d = (A_cons*(H\f)+b);
[n,m] = size(d);
x_ini = zeros(n,m);
lambda = x_ini;
al = 10;
i = 1;
%for km = 1:38
for km = 1:38
%find the elements in the solution vector one by one
% km could be larger if the Lagranger multiplier has a slow
% convergence rate.
lambda_p =lambda;
for i = 1:n
w = P(i,:) * lambda- P(i,i) * lambda(i,1);
w = w +d(i,1);
la = -w/P(i,i);
lambda(i,1) = max(0,la);
end
al=(lambda-lambda_p)' * (lambda-lambda_p);
if (al<10e-8);
break; end
end
eta = -H\f - H\A_cons'*lambda;
end