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Valid inequalities for mixed integer linear programs

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Abstract

This tutorial presents a theory of valid inequalities for mixed integer linear sets. It introduces the necessary tools from polyhedral theory and gives a geometric understanding of several classical families of valid inequalities such as lift-and-project cuts, Gomory mixed integer cuts, mixed integer rounding cuts, split cuts and intersection cuts, and it reveals the relationships between these families. The tutorial also discusses computational aspects of generating the cuts and their strength.

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Authors and Affiliations

  1. Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    Gérard Cornuéjols

  2. LIF, Faculté des Sciences de Luminy, Université d’ Aix-Marseille, 13288, Marseille, France

    Gérard Cornuéjols

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  1. Gérard Cornuéjols
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Correspondence to Gérard Cornuéjols.

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Supported by NSF grant DMI-0352885, ONR grant N00014-03-1-0188 and ANR grant BLAN06-1-138894.

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Cornuéjols, G. Valid inequalities for mixed integer linear programs. Math. Program. 112, 3–44 (2008). https://doi.org/10.1007/s10107-006-0086-0

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