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Mathematical Programming

, Volume 143, Issue 1–2, pp 111–146 | Cite as

An algorithm for the separation of two-row cuts

  • Quentin Louveaux
  • Laurent PoirrierEmail author
Full Length Paper Series A

Abstract

We consider the question of finding deep cuts from a model with two rows of the type \(P_I=\{(x,s)\in \mathbb{Z }^2\times \mathbb{R }^n_+ : x=f+Rs\}\). To do that, we show how to reduce the complexity of setting up the polar of \(\mathop {\mathrm{conv}}(P_I)\) from a quadratic number of integer hull computations to a linear number of integer hull computations. Furthermore, we present an algorithm that avoids computing all integer hulls. A polynomial running time is not guaranteed but computational results show that the algorithm runs quickly in practice.

Keywords

Integer programming Cutting planes Multi-row cuts 

Mathematics Subject Classification (2000)

90C11 

Notes

Acknowledgments

We would like to thank two anonymous referees for constructive input regarding the overall presentation and our computational experiments.

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Copyright information

© Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2012

Authors and Affiliations

  1. 1.University of LiègeLiègeBelgium

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