Hello, I am studying the following convex optimization problem and trying to translate it into CVX. I have no problems with the final two terms; it’s the logdet part that I can’t express.

(Below, A is a rectangular matrix and B is square and \lambda is a parameter; only X is unknown).

I have searched these forums and the reference guide to no avail.

If this problem is not suitable for CVX and you think of an alternative, please share! Thank you.

Proof of convexity of logdet term: X \mapsto AX^{-1}A^T + I is convex and nonincreasing on the positive definite cone, so composing it with the concave function logdet(\cdot) is again convex.