MOSEK returns NaN although the optimization problem is solved

This appears to be a bug somewhere.

Are you running CVX 3.0beta? If so, try CVX 2.1 and see what happens. Simple SDP problem has different results with different precisions I don’t believe there have been any reports yet on this forum of successful use of MOSEK 8 under CVX 3.0beta, but there have of MOSEK 8 under CVX 2.1.

I suspect the problem is on the CVX end, not the MOSEK end. But note that the latest build of MOSEK is 8.0.0.81 (you ran 8.0.0.60). I doubt it will help, but you can try.