It is well known in the area of integer linear programming that the Chvàtal-Gomory (CG) closure and the split closure of rational polyhedra are polyhedral sets.
We study the polyhedrality of these cutting plane closures when applied to general compact convex sets. We show that the CG closure of a compact convex set is a rational polytope. On the other hand, we illustrate that the split closure is not necessarily polyhedral for general convex sets. We are able to establish that the split closure can be obtained by the application of a finite number of split disjunctions for compact strictly convex sets.
This is joint work with Daniel Dadush and Juan Pablo Vielma.
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