I have the following problem.
Maximize $\sum\limits_{m=1}^M\sum\limits_{n=1}^N x_{mn}$
subject to: $\sum\limits_{\substack{m^\prime=1\\ m^\prime \neq m}}^M\sum\limits_{\substack{n^\prime=1\\ n^\prime \neq n}}^N \alpha_{mn^\prime}x_{m^\prime n^\prime} \leq \alpha_{mn},~~ \forall~ m\in\{1, 2, \cdots, M\}, \forall~ n\in\{1, 2, \cdots, N\} .$
where, $x_{mn} \in \{0, 1\}$, and $\alpha_{mn} \in \mathbb{R} ~\forall~ m\in\{1, 2, \cdots, M\}, \forall~ n\in\{1, 2, \cdots, N\}$
Please can I say that this is NP-hard problem using the fact that 0-1 integer programming is NP-hard? Is it related to knapsack problems? I know that the knapsack problem maximize the weights. For me all the weights are the same.
Thank you in advance.