Matlab MIP: Q matrix is not positive semi-definite (PSD)

[Michael]

Hello,

after working with Gurobi and Mixed integer linear programming (MILP) in Matlab for a few month I have to use mixed integer quadratic programing now.
While working on a first, simple project I get the error: "Q matrix is not positive semi-definite (PSD)" . 

The quadratic constraint causing this problem is a simple multiplication of  two variables (P = U*I) .

My code to create the matrices looks like that:

 for i = 1:n
      model.quadcon(i).Qc = sparse(zeros(n*leng,n*leng));
      model.quadcon(i).Qc(i, n+i) = 0.5;
      model.quadcon(i).Qc((n+i, i) = 0.5;
      
      model.quadcon(i).q = zeros(1,leng);
      model.quadcon(i).q(2*n+i) = -1;
      
      model.quadcon(i).rhs(1:n) = 0;
 end

I'm looking for a solution to this problem for some time now, but even though it looks like an easy task, I can't come up with a solution to turn this matrix postive semi-definite.

Is there any way I can solve this problem?

Thanks,

Michael

[Johan Löfberg]

U*I is bilinear, nonconvex and cannot be turned into a convex quadratic

Is any of the variables binary (or integer)?

[Michael]

No, unfortunately none of them is a integer variable.