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Inequalities from Group Relaxations

  1. Jean-Philippe P. Richard

Published Online: 15 FEB 2011

DOI: 10.1002/9780470400531.eorms0402

Wiley Encyclopedia of Operations Research and Management Science

Wiley Encyclopedia of Operations Research and Management Science

How to Cite

Richard, J.-P. P. 2011. Inequalities from Group Relaxations. Wiley Encyclopedia of Operations Research and Management Science. .

Author Information

  1. University of Florida, Department of Industrial and Systems Engineering, Gainesville, Florida

Publication History

  1. Published Online: 15 FEB 2011

Abstract

This article provides a review of the group-theoretic approach to the generation of cutting planes in mixed integer programming. After motivating the notion of corner relaxation graphically, we give a definition of master group problems. We then present a hierarchy of valid inequalities for master group problems that can be used as cutting planes for mixed integer programs. We describe next various procedures that can be used to obtain the “strongest” valid inequalities for master group problems. We conclude by commenting on the computational possibilities of group-theoretic cuts in mixed integer programming.

Keywords:

  • mixed integer program;
  • corner relaxation;
  • group problems;
  • group cuts;
  • valid inequalities