On the convergence of the affine hull of the Chvátal-Gomory closures

Gennadiy Averkov; Michele Conforti; Alberto Del Pia; Marco Di Summa; Yuri Faenza

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arXiv · 1210.6280

On the convergence of the affine hull of the Chvátal-Gomory closures

Gennadiy Averkov·Michele Conforti·Alberto Del Pia·Marco Di Summa·Yuri Faenza

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Abstract

Given an integral polyhedron P and a rational polyhedron Q living in the same n-dimensional space and containing the same integer points as P, we investigate how many iterations of the Chvátal-Gomory closure operator have to be performed on Q to obtain a polyhedron contained in the affine hull of P. We show that if P contains an integer point in its relative interior, then such a number of iterations can be bounded by a function depending only on n. On the other hand, we prove that if P is not full-dimensional and does not contain any integer point in its relative interior, then no finite bound on the number of iterations exists.

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Gennadiy Averkov, Michele Conforti, Alberto Del Pia, Marco Di Summa, Yuri Faenza. 2012-11-08. On the convergence of the affine hull of the Chvátal-Gomory closures. https://arxiv.org/abs/1210.6280

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