# Questions tagged [linear-programming]

Mathematical and computational method for finding the best outcome in a given mathematical model where the list of requirements is represented as linear relationships.

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### Is there a counterexample to this work?

Is there a counterexample to this claim https://arxiv.org/abs/1610.00353? They claim a $O(n^6)$ LP model with simulations to support. I think asking validity is not a reasonable problem. However ...
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### Is there a polynomial time algorithm to determine if the span of a set of matrices contains a permutation matrix?

I would like to find a polynomial time algorithm that determines if the span of a given set of matrices contains a permutation matrix. If any one knows if this problem is of a different complexity ...
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### LPs with "sparse solutions"

Consider a graph optimization on a graph with n vertices and m edges that can be written as an LP (like say bipartite matching). By the duality with vertex cover, we know that there's a sparse dual ...
Assume $P_1$, $P_2$ and $Q$ are axis-parallel polytopes in $\mathbb{R}^d$. Is it true to say that checking $CH(P_1\cup P_2)\neq Q$ is NP-hard? There is a similar result for the general polytopes but I ...