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Lift-and-Project Inequalities

  1. Quentin Louveaux

Published Online: 15 FEB 2011

DOI: 10.1002/9780470400531.eorms0463

Wiley Encyclopedia of Operations Research and Management Science

Wiley Encyclopedia of Operations Research and Management Science

How to Cite

Louveaux, Q. 2011. Lift-and-Project Inequalities. Wiley Encyclopedia of Operations Research and Management Science. .

Author Information

  1. University of Liège, Montefiore Institute, Liège, Belgium

Publication History

  1. Published Online: 15 FEB 2011

Abstract

The lift-and-project technique is a systematic way to generate valid inequalities for a mixed binary program. The technique is interesting both on the theoretical and on the practical point of view. On the theoretical side it allows one to construct the inequality description of the convex hull of all mixed-{0, 1} solutions of a binary mixed-integer program (MIP) in n repeated applications of the technique, where n is the number of binary variables. On the practical side, a variant of the method allows one to derive some cutting planes from the simplex tableau rather efficiently.

Keywords:

  • lift-and-project;
  • polyhedra projection;
  • disjunctive inequality;
  • CGLP;
  • MIP