The Gomory-Chvátal Closure of a Non-Rational Polytope is a Rational Polytope

Juliane Dunkel () and Andreas S. Schulz ()
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Juliane Dunkel: Massachusetts Institute of Technology
Andreas S. Schulz: Massachusetts Institute of Technology

A chapter in Operations Research Proceedings 2011, 2012, pp 587-592 from Springer

Abstract: Abstract The question as to whether the Gomory-Chvátal 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: Convex Body; Valid Inequality; Integral Vector; Rational Polyhedron; Polyhedral Theory (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-3-642-29210-1_93

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