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The Gomory-Chvatal closure of a non-rational polytope is a rational polytope

Dunkel (juliane***at***mit.edu)
Schulz (schulz***at***mit.edu)

Abstract: The question as to whether the Gomory-Chvatal closure of a non-rational polytope is a polytope has been a longstanding open problem in integer programming. In this paper, we answer this question in the affirmative, by combining ideas from polyhedral theory and the geometry of numbers.

Keywords: Gomory-Chvatal closure, polytopes, integer programming, lattices, reduced bases

Category 1: Integer Programming

Category 2: Integer Programming (Cutting Plane Approaches )


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Entry Submitted: 11/08/2010
Entry Accepted: 11/08/2010
Entry Last Modified: 03/24/2011

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