Split Closure and Intersection Cuts

Abstract

In the seventies, Balas introduced intersection cuts for a Mixed Integer Linear Program (MILP), and showed that these cuts can be obtained by a closed form formula from a basis of the standard linear programming relaxation. In the early nineties, Cook, Kannan and Schrijver introduced the split closure of an MILP, and showed that the split closure is a polyhedron. In this paper, we show that the split closure can be obtained using only intersection cuts. We give two different proofs of this result, one geometric and one algebraic. Furthermore, the result is used to provide a new proof of the fact that the split closure is a polyhedron. Finally, we extend the result to more general two-term disjunctions.KeywordsMixed Integer Linear ProgramValid InequalityEarly NinetyClosed Form FormulaSplit ClosureThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.