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Unique lifting of integer variables in minimal inequalities

Basu, Amitabh , Campelo, Manoel B., Conforti, Michele, Cornuéjols, Gérard and Zambelli, Giacomo (2012) Unique lifting of integer variables in minimal inequalities. Mathematical Programming, Online . ISSN 0025-5610

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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; they are derived using the gauge function of maximal lattice-free convex sets. 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 (This result first appeared in the proceedings of IPCO 2010). The answer is a nonconvex region that can be obtained as a finite union of convex polyhedra. We then establish a necessary and sufficient condition for the uniqueness of the lifting function.

Item Type: Article
Official URL: http://www.springerlink.com/content/0025-5610/
Additional Information: © 2012 Springer and Mathematical Optimization Society.
Library of Congress subject classification: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Sets: Departments > Management
Research centres and groups > Management Science Group
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 27 Jun 2012 13:45
URL: http://eprints.lse.ac.uk/44493/

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