How to write log(1+Ax)? A are two constant

You are showing 2 different Mosek outputs. What is the difference between the problems you’re solving?

The first was solved to optimality, but the optimal objective value of 2e10 is indicative of very bad numerical scaling.

In the second, Mosek issues warning about nearly zero elements in the input data. Mosek reports dual infeasibility, but it was provided the dual, so I think that should correspond to primal unbounded, yet CVX reports it as (primal( infeasible. This seems to be the same thing as happened in How to minimize the largest singular value of the matrix , So I don’t know whether this is really infeasible or unbounded. Nevertheless, I suggest you improve scaling (by changing units) so that all input data is within s small number of orders of magnitude of 1, then re-run it and see what Mosek and CvX report.