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

  • Jean-Philippe P. Richard
  • Ismael R. de FariasJr
  • George L. Nemhauser
Conference paper
Part of the Lecture Notes in Computer Science book series (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.

Keywords

Mixed Integer Mixed Integer Programming Valid Inequality Georgia Institute Lift Scheme 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Jean-Philippe P. Richard
    • 1
  • Ismael R. de FariasJr
    • 2
  • George L. Nemhauser
    • 3
  1. 1.School of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlantaUSA
  2. 2.Center for Operations Research and EconometricsLouvain-La-NeuveBelgium
  3. 3.School of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlantaUSA

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