On lifting integer variables in minimal inequalities

Authors:
Amitabh Basu;Manoel Campelo;Michele Conforti;Gérard Cornuéjols;Giacomo Zambelli
Affiliations:
Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA;Departamento de Estatística e Matemática Aplicada, Universidade Federal do Ceará, Brazil;Dipartimento di Matematica Pura e Applicata, Universitá di Padova, Padova, Italy;Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA;Dipartimento di Matematica Pura e Applicata, Universitá di Padova, Padova, Italy
Venue:
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Year:
2010

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Abstract

This paper contributes to the theory of cutting planes for mixed integer linear programs (MILPs). Minimal valid inequalities are well understood for a relaxation of an MILP in tableau form where all the nonbasic variables are continuous. In this paper we study lifting functions for the nonbasic integer variables starting from such minimal valid inequalities. We characterize precisely when the lifted coefficient is equal to the coefficient of the corresponding continuous variable in every minimal lifting. The answer is a nonconvex region that can be obtained as the union of convex polyhedra.