If you have Mosek (10.x or 9.x) available as solver, use that ((preferably 10.x). if not, follow the directions at CVXQUAD: How to use CVXQUAD's Pade Approximant instead of CVX's unreliable Successive Approximation for GP mode, log, exp, entr, rel_entr, kl_div, log_det, det_rootn, exponential cone. CVXQUAD's Quantum (Matrix) Entropy & Matrix Log related functions .
It may be that your input data is badly scaled numerically. Change units if necessary so that all non-zero input data is within a small number of orders of magnitude of 1. Maybe some of the numbers in data are` tiny, and should be set to be exactly zero, or their differences are tiny, and those differences should be set to exactly zero? Perhaps the objective is coupling into the constraint to make is appear numerically infeasible, even though the problem is clearly feasible.