Basically, I have proved that the constraint (9b) is convex given the constraints. However, I cannot let the CVX recognize it is a convex constraint. I tried to utilize the rel_entr function but finally failed. Do anyone know how to transfer the constraint to let CVX recognize it is actually convex?

It doesn’t appear to be either convex or concave over the entirety of its natural domain. Therefore, it seems unlikely there will be a CVX representation, even if it is convex in the constraint region.

Thank you again for your reply. Do you have any ideas to transform this problem, so that this problem can be solved with existing solvers? It seems still difficult even using block coordinate descent. For example, when I fix the optimization variables q and t, I still cannot use CVX to solve the problem since it appears A\rho /(B-C*log(\rho-1)).