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Reformulation-Linearization Technique for MIPs

  1. Hanif D. Sherali

Published Online: 15 FEB 2011

DOI: 10.1002/9780470400531.eorms0712

Wiley Encyclopedia of Operations Research and Management Science

Wiley Encyclopedia of Operations Research and Management Science

How to Cite

Sherali, H. D. 2011. Reformulation-Linearization Technique for MIPs. Wiley Encyclopedia of Operations Research and Management Science. .

Author Information

  1. Virginia Polytechnic Institute and State University, Grado Department of Industrial and Systems Engineering, Blacksburg, Virginia

Publication History

  1. Published Online: 15 FEB 2011

Abstract

The reformulation-linearization technique (RLT) for mixed-integer programs is an automatic model enhancement approach that generates a hierarchy of relaxations spanning the spectrum from the continuous linear programming (LP) relaxation to the convex hull of feasible solutions. This process is applicable to both 0-1 as well as general discrete programs, and can be further augmented through the use of classes of semidefinite cuts. Often, the first-level relaxation itself provides a sufficiently tight model reformulation that significantly improves problem solvability. The RLT procedure also offers a unifying framework for solving continuous nonconvex factorable optimization problems to global optimality.

Keywords:

  • reformulation-linearization technique;
  • RLT;
  • mixed-integer programming;
  • lift-and-project;
  • tight relaxations;
  • valid inequalities;
  • model reformulation;
  • convex hull;
  • nonconvex programs;
  • global optimization