with respect to the matrix X. A, B and C are matrices, where B, C and (B - XCX’) are positive semidefinite.

Is there a way of formulating this problem using the DCP ruleset so that CVX can solve it? I was thinking about adding the constraint that B - XCX’ is SDP via the Schur complement, such that CVX knows the problem is convex…

Thanks for your fast reply. I agree that in general this as a non-convex problem. My thought was that with the additional constraint of the matrix (B - XCX’) being PSD the problem is convex on the restricted domain. Please correct me if I made a mistake here.