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 lin-ear 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 clo-sure can be obtained using only intersection cuts. We give two dierent 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.