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For questions about mathematical optimization problems involving both continuous and binary or general integer variables.
0
votes
Free solver for MINP problems
You can check the NEOS Server which provides free solvers for mixed-integer nonlinear programming (MINLP) problems. You can use solvers like Bonmin or Couenne via their web-based platform.
1
vote
Removing min operator from max objective
A simple intuition would be that the second inequality is stronger ($\geq$) than the first one. Therefore, dropping the minimum would allow more flexibility, but I do not think they are equivalent.
2
votes
Accepted
Why is the convex hull of a integer linear program a polyhedron with same optimum?
You can apply the convex hull's definition to an optimal solution $ x^* $. It can be written as:
$$ x^* = \sum_{1 \leq k \leq m} \lambda_k x_k $$
such that $ \lambda_k \geq 0 $, $ \sum_{1 \leq k \leq …