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Valid inequalities for MIPs and group polyhedra from approximate liftings

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Abstract

In this paper, we present an approximate lifting scheme to derive valid inequalities for general mixed integer programs and for the group problem. This scheme uses superadditive functions as the building block of integer and continuous lifting procedures. It yields a simple derivation of new and known families of cuts that correspond to extreme inequalities for group problems. This new approximate lifting approach is constructive and potentially efficient in computation.

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Authors and Affiliations

  1. School of Industrial Engineering, Purdue University, 315 N. Grant Street, West Lafayette, IN, 47907-2023, USA

    Jean-Philippe P. Richard

  2. Krannert School of Management, Purdue University, 403 W. State Street, West Lafayette, IN, 47907-2056, USA

    Yanjun Li

  3. Department of Mechanical Engineering, University of Minnesota, 111 Church Street S.E., Minneapolis, MN, 55455, USA

    Lisa A. Miller

Authors
  1. Jean-Philippe P. Richard
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  2. Yanjun Li
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  3. Lisa A. Miller
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Correspondence to Jean-Philippe P. Richard.

Additional information

J.-P. P. Richard was supported by NSF grant DMI-348611.

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Richard, JP.P., Li, Y. & Miller, L.A. Valid inequalities for MIPs and group polyhedra from approximate liftings. Math. Program. 118, 253–277 (2009). https://doi.org/10.1007/s10107-007-0190-9

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  • DOI: https://doi.org/10.1007/s10107-007-0190-9

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