Mathematical Programming Computation

, Volume 11, Issue 2, pp 211–235 | Cite as

The (not so) trivial lifting in two dimensions

  • Ricardo Fukasawa
  • Laurent Poirrier
  • Álinson S. XavierEmail author
Full Length Paper


When generating cutting-planes for mixed-integer programs from multiple rows of the simplex tableau, the usual approach has been to relax the integrality of the non-basic variables, compute an intersection cut, then strengthen the cut coefficients corresponding to integral non-basic variables using the so-called trivial lifting procedure. Although of polynomial-time complexity in theory, this lifting procedure can be computationally costly in practice. For the case of two-row relaxations, we present a practical algorithm that computes trivial lifting coefficients in constant time, for arbitrary maximal lattice-free sets. Computational experiments confirm that the algorithm works well in practice.


Integer programming Lifting Cutting planes 

Mathematics Subject Classification

90C11 90C57 

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature and The Mathematical Programming Society 2018

Authors and Affiliations

  • Ricardo Fukasawa
    • 1
  • Laurent Poirrier
    • 1
  • Álinson S. Xavier
    • 2
    Email author
  1. 1.Department of Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada
  2. 2.Energy Systems DivisionArgonne National LaboratoryLemontUSA

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