论文信息 - A constructive characterization of the split closure of a mixed integer linear program

A constructive characterization of the split closure of a mixed integer linear program

Two independent proofs of the polyhedrality of the split closure of mixed integer linear program have been previously presented. Unfortunately neither of these proofs is constructive. In this paper, we present a constructive version of this proof. We also show that split cuts dominate a family of inequalities introduced by Koppe and Weismantel.

Juan Pablo Vielma

[1] William J. Cook,et al. Chvátal closures for mixed integer programming problems , 1990, Math. Program..

[2] Laurence A. Wolsey,et al. Integer and Combinatorial Optimization , 1988 .

[3] Alberto Caprara,et al. On the separation of split cuts and related inequalities , 2003, Math. Program..

[4] Egon Balas,et al. programming: Properties of the convex hull of feasible points * , 1998 .

[5] Michael J. Todd,et al. Mathematical programming , 2004, Handbook of Discrete and Computational Geometry, 2nd Ed..

[6] G. Ziegler. Lectures on Polytopes , 1994 .

[7] Egon Balas,et al. Intersection Cuts - A New Type of Cutting Planes for Integer Programming , 1971, Oper. Res..

[8] Kent Andersen,et al. Split closure and intersection cuts , 2002, Math. Program..

[9] Egon Balas,et al. A precise correspondence between lift-and-project cuts, simple disjunctive cuts, and mixed integer gomory cuts for 0-1 programming , 2003, Math. Program..

[10] Matthias Köppe,et al. Cutting planes from a mixed integer Farkas lemma , 2004, Oper. Res. Lett..

[11] G. Nemhauser,et al. Integer Programming , 2020 .

[12] Dimitris Bertsimas,et al. Optimization over integers , 2005 .

[13] Andrea Lodi,et al. On the MIR Closure of Polyhedra , 2007, IPCO.

[14] Egon Balas,et al. Optimizing over the split closure , 2008, Math. Program..