The split closure of a strictly convex body |
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| Authors: | D. Dadush |
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| Affiliation: | a H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, 765 Ferst Drive NW, Atlanta, GA 30332-0205, United Statesb Business Analytics and Mathematical Sciences Department, IBM T. J. Watson Research Center, P.O. Box 218, Yorktown Heights, NY 10598, United Statesc Department of Industrial Engineering, University of Pittsburgh 1048 Benedum Hall, Pittsburgh, PA 15261, United States |
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| Abstract: | The Chvátal-Gomory closure and the split closure of a rational polyhedron are rational polyhedra. It has been recently shown that the Chvátal-Gomory closure of a strictly convex body is also a rational polytope. In this note, we show that the split closure of a strictly convex body is defined by a finite number of split disjunctions, but is not necessarily polyhedral. We also give a closed form expression in the original variable space of a split cut for full-dimensional ellipsoids. |
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| Keywords: | Split cuts Split closure Nonlinear integer programming |
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