A discrete Farkas lemma

A discrete Farkas lemma

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Article ID: iaor2005388
Country: Netherlands
Volume: 1
Issue: 1
Start Page Number: 67
End Page Number: 75
Publication Date: Jun 2004
Journal: Discrete Optimization
Authors:
Keywords: programming: linear
Abstract:

Given A ∈ ℤm×n and b ∈ ℤm, we consider the issue of existence of a solution x ∈ ℕn to the system of linear equations Ax=b. We provide a discrete analogue of the celebrated Farkas lemma for linear systems in n and prove that checking existence of integral solutions reduces to solving an explicit linear programming problem of fixed dimension, known in advance.

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