The Gomory-Chvátal closure of a nonrational polytope is a rational polytope. (English) Zbl 1291.90142
Summary: 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.