Mathematical Methods of Operations Research

, Volume 53, Issue 2, pp 173–203 | Cite as

Classical cuts for mixed-integer programming and branch-and-cut

  • Manfred Padberg


We review classical valid linear inequalities for mixed-integer programming, i.e., Gomory's fractional and mixed-integer cuts, and discuss their use in branch-and-cut. In particular, a generalization of the recent mixed-integer rounding (MIR) inequality and a sufficient condition for the global validity of classical cuts after branching has occurred are derived.

Key words: Mixed-integer programming cutting planes Gomory cuts branch-and-cut 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Manfred Padberg
    • 1
  1. 1.17, rue Vendôme, 13007 Marseille, FranceFR

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