Mathematical Programming

, Volume 112, Issue 1, pp 3–44

Valid inequalities for mixed integer linear programs


DOI: 10.1007/s10107-006-0086-0

Cite this article as:
Cornuéjols, G. Math. Program. (2008) 112: 3. doi:10.1007/s10107-006-0086-0


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.


Mixed integer linear programLift-and-projectSplit cutGomory cutMixed integer roundingElementary closurePolyhedraUnion of polyhedra

Mathematics Subject Classification (2000)


Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Tepper School of BusinessCarnegie Mellon UniversityPittsburghUSA
  2. 2.LIF, Faculté des Sciences de LuminyUniversité d’ Aix-MarseilleMarseilleFrance