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 (*I _{m} + H X H’*)

**subject to**

*X*Hermitian

*n*-times-

*n*positive semidefinite

trace(

*E*) ≤

_{i}X*a*

_{i}, i = 1,…,mwhere *I _{m}* is the m-dimensional identity matrix,

*H*is a

*m*-times-

*n*complex matrix, E

_{i}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?

Cheers,

Emanuele