The problem is to maximize concave objective function with convex constraints:
$\max \sum_{i=1}^{N} \sum_{j=1}^{M} log_2{(1+ x_{ij}c_{ij})}$
subject to $\sum_{j=1}^{M} x_{ij}g_{ij} \leq a_{i}, \forall i,$
$\sum_{i=1}^{N} x_{ij} \leq b, \forall j,$
$0 \leq x_{ij} \leq b$,
$c_{ij}, g_{ij},a_{i}, b$ are nonnegative real values and are known, $x_{ij}$-control variable. Range of $c_{ij}:1 -10^9$,$g_{ij}:10^{-14} -10^{-7}$,$a_{i}:10^{-12} -10^{-9}$,$b=10^{-3}$. I tried to solve this using CVX, but for some instances, it is giving a NaN solution. Are there any other methods or solvers that can solve this problem?