I have the following optimization problem.
$$ \max_{x_{ij}} \sum_{i=1}^{N} \sum_{j=1}^{M} x_{ij} \log_2 \left(\frac{P y_{ij}}{\sum_{i=1}^{N}x_{ij}}\right)\\ \text{s.t.} \sum_{j=1}^{M} \frac{P x_{ij} g_{ij}}{\sum_{i=1}^{N}x_{ij}} \leq a_{i}, \forall i,\\ x_{ij} \in \{ 0,1\} $$
here, $y_{ij},P, g_{ij}, a_{i}$ are real values which are known. How to approach this binary nonlinear problem. Thanks in advance.