NDLI: On the Convergence of the Affine Hull of the Chvátal--Gomory Closures

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Conforti, Michele Di Summa, Marco Faenza, Yuri Averkov, Gennadiy Del Pia, Alberto
Copyright Year	2013
Abstract	Given an integral polyhedron $P\subseteq\mathbb{R}^n$ and a rational polyhedron $Q\subseteq\mathbb{R}^n$ 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.
Starting Page	1492
Ending Page	1502
Page Count	11
File Format	PDF
ISSN	08954801
DOI	10.1137/120898371
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	3
Volume Number	27
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2013-09-04
Access Restriction	Subscribed
Subject Keyword	Integer programming Lattice polytopes Lattices and convex bodies in $n$ dimensions Chvátal rank Chvátal--Gomory closure affine hull cutting plane integral polyhedron
Content Type	Text
Resource Type	Article
Subject	Mathematics

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On the Convergence of the Affine Hull of the Chvátal--Gomory Closures