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Lifted inequalities for 0-1 mixed integer programming: Basic theory and algorithms

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Abstract.

We study the mixed 0-1 knapsack polytope, which is defined by a single knapsack constraint that contains 0-1 and bounded continuous variables. We develop a lifting theory for the continuous variables. In particular, we present a pseudo-polynomial algorithm for the sequential lifting of the continuous variables and we discuss its practical use.

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Authors and Affiliations

  1. School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, 30332-0205, USA

    J.-P.P. Richard

  2. Center for Operations Research and Econometrics, 34 Voie du Roman Pays, 1348, Louvain-La-Neuve, Belgium

    I.R. de Farias Jr

  3. School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, 30332-0205, USA

    G.L. Nemhauser

Authors
  1. J.-P.P. Richard
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  2. I.R. de Farias Jr
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  3. G.L. Nemhauser
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Correspondence to J.-P.P. Richard.

Additional information

This research was supported by NSF grants DMI-0100020 and DMI-0121495

Mathematics Subject Classification (2000): 90C11, 90C27

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Richard, JP., de Farias Jr, I. & Nemhauser, G. Lifted inequalities for 0-1 mixed integer programming: Basic theory and algorithms. Math. Program., Ser. B 98, 89–113 (2003). https://doi.org/10.1007/s10107-003-0398-2

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  • DOI: https://doi.org/10.1007/s10107-003-0398-2

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