The split closure of a strictly convex body

The Chv´atal-Gomory closure and the split closure of a rational polyhedron are rational polyhedra. It was recently shown that the Chv´atal-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.

• Type: Journal
• Year: 2011
• Where: ORL
• Authors: D. Dadush, Santanu S. Dey, Juan Pablo Vielma
• Keywords: Chv´atal-Gomory Closure, Convex Body, Operations Research, ORL 2011, Split Closure