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Lifted Inequalities for 0-1 Mixed Integer Programming: Basic Theory and Algorithms

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Integer Programming and Combinatorial Optimization (IPCO 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2337))

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. We introduce the concept of super-linear inequalities and show that our lifting scheme can be significantly simplified for them. Finally, we show that superlinearity results can be generalized to nonsuperlinear inequalities when the coefficients of the continuous variables lifted are large.

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

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Author information

Authors and Affiliations

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

    Jean-Philippe P. Richard

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

    Ismael R. de Farias Jr

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

    George L. Nemhauser

Authors
  1. Jean-Philippe P. Richard
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  2. Ismael R. de Farias Jr
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  3. George L. Nemhauser
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Editor information

Editors and Affiliations

  1. Program in Applied and Computational Mathematics, University of Princeton, Fine Hall, Washington Road, Princeton, NJ, 08544-1000, USA

    William J. Cook

  2. Sloan School of Management, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA, 02139-4307, USA

    Andreas S. Schulz

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© 2002 Springer-Verlag Berlin Heidelberg

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Richard, JP.P., de Farias, I.R., Nemhauser, G.L. (2002). Lifted Inequalities for 0-1 Mixed Integer Programming: Basic Theory and Algorithms. In: Cook, W.J., Schulz, A.S. (eds) Integer Programming and Combinatorial Optimization. IPCO 2002. Lecture Notes in Computer Science, vol 2337. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47867-1_12

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  • DOI: https://doi.org/10.1007/3-540-47867-1_12

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43676-8

  • Online ISBN: 978-3-540-47867-6

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