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. © 2010 Springer-Verlag.
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CITATION STYLE
Basu, A., Campelo, M., Conforti, M., Cornuéjols, G., & Zambelli, G. (2010). On lifting integer variables in minimal inequalities. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6080 LNCS, pp. 85–95). https://doi.org/10.1007/978-3-642-13036-6_7
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