Semi-definite programming with large matrices

I’m new to CVX.
My problem has the following form

cvx_begin sdp
variable P(n,n)
minimize(norm(P*D1 - D2*P))

% here are few linear matrix inequalities


It works well for small matrices less than 100x100. However, I need at least twice bigger matrices, and when n is greater than 100 it crashes, usually with the low memory error. I tried to use default solver and Mosek.

Is there some fundamental problem with solving SDP for large matrices or maybe I’m doing something wrong ?

I have very little experience with convex programming so any help will be greatly appreciated :blush:

I’m afraid semidefinite programming is simply expensive.