I have 10000 variables (each of them is binary), vector of positive coefficients and a matrix $A$ ($10000\times10000$), if $A_{ij}=1$, then $i$th and $j$th variables can take 1 simultaneously, if it is 0, then it is not possible. The goal is to maximize their weighted sum. What algorithms and software could I use to solve this problem?
\begin{array}{l} \max F\left( x_{1}..x_{m} \right)=\sum\limits_{i=1}^m {b_{i}x_{i}} \end{array}
\begin{array}{l} x_{i}\in \left\{ 0,1 \right\},\, \, i=1..m \\ x_{i}x_{j}\le A_{ij}\,, i,j=1..m \\ A_{ij}\in \left\{ 0,1 \right\},\, \, i,j=1..m \\ \end{array}