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