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.
| Original language | English (US) |
|---|---|
| Title of host publication | Wiley Encyclopedia of Operations Research and Management Science |
| Publisher | Wiley |
| Pages | 1-13 |
| Number of pages | 13 |
| ISBN (Electronic) | 9780470400531 |
| ISBN (Print) | 9780470400630 |
| DOIs | |
| State | Published - Jan 1 2010 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2010 John Wiley & Sons, Inc. All rights reserved.
Keywords
- corner relaxation
- group cuts
- group problems
- mixed integer program
- valid inequalities
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