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A 3-Slope Theorem for the infinite relaxation in the plane

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Abstract

In this paper we consider the infinite relaxation of the corner polyhedron with 2 rows. For the 1-row case, Gomory and Johnson proved in their seminal paper a sufficient condition for a minimal function to be extreme, the celebrated 2-Slope Theorem. Despite increased interest in understanding the multiple row setting, no generalization of this theorem was known for this case. We present an extension of the 2-Slope Theorem for the case of 2 rows by showing that minimal 3-slope functions satisfying an additional regularity condition are facets (and hence extreme). Moreover, we show that this regularity condition is necessary, unveiling a structure which is only present in the multi-row setting.

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Authors and Affiliations

  1. Carnegie Mellon University, 5000 Forbes Ave, Pittsburgh, PA, 15213, USA

    Gérard Cornuéjols & Marco Molinaro

Authors
  1. Gérard Cornuéjols
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  2. Marco Molinaro
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Correspondence to Marco Molinaro.

Additional information

Supported by NSF grant CMMI1024554 and ONR grant N00014-09-1-0033.

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Cornuéjols, G., Molinaro, M. A 3-Slope Theorem for the infinite relaxation in the plane. Math. Program. 142, 83–105 (2013). https://doi.org/10.1007/s10107-012-0562-7

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  • DOI: https://doi.org/10.1007/s10107-012-0562-7

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