I am trying to solve a linear program with more than $7$ million constraints in around $5000$ variables. It could not be solved on my computer. In the constraints, there is overlap, e.g.,
$$ \begin{aligned} 2X_1 + 3X_2 &\leq 5 \\ 1X_1 + 2X_2 &\leq 5 \end{aligned} $$
In this example, it is pretty clear that the second constraint is dominated by the first constraint because if the first constraint is smaller than $5$ then automatically the second constraint is smaller than $5$. But some examples are not that easy to identify, for example, if a constraint is dominated by a combination of other constraints. Does someone have an idea how I could find all the unnecessary constraints to reduce the number of constraints in the linear program (all the variables should be larger than $0$).