On the Chvátal-Gomory closure of a compact convex set

Authors:
Daniel Dadush;Santanu S. Dey;Juan Pablo Vielma
Affiliations:
H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA;H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA;Department of Industrial Engineering, University of Pittsburgh, Pittsburgh, PA
Venue:
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Year:
2011

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Abstract

In this paper, we show that the Chvátal-Gomory closure of any compact convex set is a rational polytope. This resolves an open question of Schrijver [15] for irrational polytopes, and generalizes the same result for the case of rational polytopes [15], rational ellipsoids [7] and strictly convex bodies [6].