I believe that other then some constant multiplicative factors, 1/sum_inv_P_total_times_T is a harmonic mean, which is concave, and can be handled as shown in section 3,2,7 “Harmonic mean” of 3 Conic quadratic optimization — MOSEK Modeling Cookbook 3.3.0 .However, I have no reason to believe that the objective function, which multiplies that by sum(Q_total) is concave. So your first task is to prove that the objective function is concave. If not, CVX is not the right tool for the problem.