How to solve minimization problem with unconvex constrains as follows with cvx:
min~~y
f(\{x_k^l\}) \le y;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~k=1:K,l=1:L;
\ln \sum_n (q_n^l w_n^k)-\ln \sum_n (q_n^l) \le x_k^l;~~~~~~k=1:K, l=1:L;
\sum_l \ln (1-q_n^l) \le \ln r_n,~~~~~~~~~~~~~~~~~~~~~~~~n=1:N
0 \le q_n^l \le 1,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~n=1:N, l=1:L;
f(\{x_k^l\}): increasing function, convex
This is non-convex. Are you expecting a miracle?
Sorry for that. I am just wondering whether there are some reformulation ways to turn it into a convex problem.
The only hope I can see is if the combination (intersection) of constraints somehow defines a convex region, which would introduce the hope of creating a formulation acceptable to CVX. If that’s the case, you need to prove at least that the intersection of constraints is convex. I assume it is not.
As the FAQ says: if your model is not convex, you should not be using CVX. I really don’t know how we can be any plainer than that.