Singular KKT Matrix

[Alireza]

Dear professor

I have a problem in inequality Constrained Quadratic Programming in following form  and I wish you help me with your valuable advice.

min 0.5 x' G x + f'x

s.t Ax>b

I am trying to solve the problem using KKT conditions and primal active set method.

in my problem G is semi-positive definite and the eigenvalues of G is 0 , 0 ,0, 1 , 1 ,1 and A is full rank matrix.

When i try to solve the problem with active set method the KKT Matrix is being singular and the algorithm cant apply.I had tried the pseudo inverse but comparing to state - of - the-art solvers base on active set method my code has not reliable solution except when on of eigenvalues was zero. for more than one zero eigenvalue I can't find solution and pseudo inverse is useless I think.

simply saying the algorithm for SPD matrix G is working (using pseudo inverse ) only when there is just one zero eigenvalue.

how can I deal with this kind of problem ?

Many thanks 

Best

Alireza

[Johan Löfberg]

You are posting the question on the wrong forum.

[Alireza]

would you please answer just this question.I promise  never ask unrelated questions.

[Erling D. Andersen]

Why do not just use an interior-point method like https://mosek.com.

[Alireza]

No .since my problem is small the active set is faster than IP .
Thanks for the comment

[Erling D. Andersen]

Since the active set cannot solve your problems then I do not think the active set method is that fast.

[Alireza]

since Matlab solver based on active set works correct The problem is not from the method and it is from my code.but I can not figure out how to fix it