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The Structure of the Infinite Models in Integer Programming

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Integer Programming and Combinatorial Optimization (IPCO 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10328))

Abstract

The infinite models in integer programming can be described as the convex hull of some points or as the intersection of halfspaces derived from valid functions. In this paper we study the relationships between these two descriptions. Our results have implications for finite dimensional corner polyhedra. One consequence is that nonnegative continuous functions suffice to describe finite dimensional corner polyhedra with rational data. We also discover new facts about corner polyhedra with non-rational data.

A. Basu and J. Paat—Supported by the NSF grant CMMI1452820.

M. Conforti and M. Di Summa—Supported by the grant “Progetto di Ateneo 2013”.

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Notes

  1. 1.

    Such results are obtainable in the case \(n=1\) by more elementary means such as interpolation. We are unaware of a way to establish these results for general \(n\ge 2\) without using the technology developed in this paper.

  2. 2.

    For an explicit construction of such a function, see the journal version of the paper.

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Authors and Affiliations

  1. Department of Applied Mathematics and Statistics, The Johns Hopkins University, Baltimore, USA

    Amitabh Basu & Joseph Paat

  2. Dipartimento di Matematica, Università degli Studi di Padova, Padua, Italy

    Michele Conforti & Marco Di Summa

Authors
  1. Amitabh Basu
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  2. Michele Conforti
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  3. Marco Di Summa
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  4. Joseph Paat
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Corresponding author

Correspondence to Marco Di Summa .

Editor information

Editors and Affiliations

  1. Ecole Polytechnique Federale de Lausanne - EPFL, Lausanne, Switzerland

    Friedrich Eisenbrand

  2. University of Waterloo, Waterloo, Ontario, Canada

    Jochen Koenemann

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Basu, A., Conforti, M., Di Summa, M., Paat, J. (2017). The Structure of the Infinite Models in Integer Programming. In: Eisenbrand, F., Koenemann, J. (eds) Integer Programming and Combinatorial Optimization. IPCO 2017. Lecture Notes in Computer Science(), vol 10328. Springer, Cham. https://doi.org/10.1007/978-3-319-59250-3_6

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  • DOI: https://doi.org/10.1007/978-3-319-59250-3_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-59249-7

  • Online ISBN: 978-3-319-59250-3

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