CVX with large max-det problems

Good afternoon to everybody, and thanks in advance for any possible answer.

I have the following entropy maximization problem (log det maximization with linear inequality constraints):

maximize    log_det (Im + H X H’)
subject to   X Hermitian n-times-n positive semidefinite
          trace(Ei X) ≤ ai,  i = 1,…,m

where Im is the m-dimensional identity matrix, H is a m-times-n complex matrix, Ei are n-times-n Hermitian positive semidefinite matrices and ( · )’ stands for conjugate transpose. I tried to use CVX (with standard license), but Matlab runs out of memory (“array exceeds maximum array size preference”) for n = 200 and m = 100 (and I would need larger values).

Unfortunately, I am not an expert in convex optimization nor an advanced user of CVX, so my questions are:

  • Is n = 200 a very large value for this kind of problems?
  • Can CVX can handle it, or the memory problem is just related to my hardware/software?
  • If it is actually too large, are there some specialized solvers that can handle it?


I just realized that I can solve the problem (semi-)analytically: I will use CVX to test the solution for small values of n and m.