Why is the result of CVX running different from what I theoretically derived?

Mosek reports that the problem is dual ill-posed. CVX provided Mosek the dual of the original problem, so that means Mosek concluded that your problem is primal ill-posed,.

I ran the problem using Mosek 10.1.17, and it solved to claimed optimality, with cvx_optval = 49.2817. The Mosek solver has become more robust since Mosek 9.1.9, so perhaps that’s why my run succeeded and yours didn’t.

You should also use the latest version of Mosek 10.x, rather than 9.1.9 which is bundled with CVX. In order to do so, follow the directions in