Split closure and intersection cuts

Authors:
Kent Andersen;Gérard Cornuéjols;Yanjun Li
Affiliations:
Tepper School of Business, Carnegie Mellon University, 15213, Pittsburgh, PA, USA;Tepper School of Business, Carnegie Mellon University, 15213, Pittsburgh, PA, USA and LIF, University of Marseille at Luminy, 13288, Marseille, France;Krannert Graduate School of Management, Purdue University, 47907, West Lafayette, IN, USA
Venue:
Mathematical Programming: Series A and B
Year:
2005

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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 a 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. The result is then used to provide a new proof of the fact that the split closure of a MILP is a polyhedron. Finally, we extend the result to more general disjunctions.