The split closure of a strictly convex body

• DOI: 10.1016/j.orl.2011.02.002
• Publication Date: 2011-02-11T09:27:27Z
• Authors: D. Dadush; S.S. Dey; J.P. Vielma
• Keywords: Polyhedron; Convex polytope; Closure (psychology); Ellipsoid

The Chvatal-Gomory closure and the split closure of a rational polyhedron are rational polyhedra. It has been recently shown that the Chvatal-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.