We have no idea what your program is, other than that it involves a function utilizing the exponential cone.
If you have access to Mosek as solver, use it. Otherwise 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 also be the case that the numerical scaling in your problem is poor.