I haven’t checked to determine whether your program is correct. (Perhaps you’ve already seen http://web.cvxr.com/cvx/examples/cvxbook/Ch07_statistical_estim/html/logistics.html and http://web.cvxr.com/cvx/examples/cvxbook/Ch07_statistical_estim/html/logistics_gp.html )
Presuming your formulation is “good”, you are still subject to the limitations of CVX’s successive approximation method - read the discliamers at http://cvxr.com/cvx/doc/advanced.html#the-successive-approximation-method . You can avoid using CVX’s successive approximation method by installing CVXQUAD https://github.com/hfawzi/cvxquad and the exponential.m replacement for CVX’s version, as discussed at the link. This will invoke CVXQUAD’s Pade Appoximant method and avoid use of CVX’s successive approximation method for Geometric Programming mode, and for certain log and exp related functions, such as entr and rel_entr, log_sum_exp, and I think should automatically be invoked for log(sum(exp(…))) as you have. If it is invoked, you should see a message “Using Pade approximation for exponential cone with parameters m=3, k=3” Please remove cvx_expert true from your program. If you see that the successive approximation method was invoked, you may need some reformulation of your program in ordrer to get it invoked. If CVXQUAD’s Pade approximation is invoked instead of CVX’s successive approximation method, the solution should be more reliable, and hopefully succeed, unless you have a poorly formulated problem.
Edit: Note that I fixed the link to CVXQUAD, which is https://github.com/hfawzi/cvxquad .