The Gomory-Chvátal Closure of a Nonrational Polytope Is a Rational Polytope

Authors:
Juliane Dunkel;Andreas S. Schulz
Affiliations:
Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139;Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Venue:
Mathematics of Operations Research
Year:
2013

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Abstract

The question as to whether the Gomory-Chvátal closure of a nonrational 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.