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The projected faces property and polyhedral relations

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Abstract

Margot (1994) in his doctoral dissertation studied extended formulations of combinatorial polytopes that arise from “smaller” polytopes via some composition rule. He introduced the “projected faces property” of a polytope and showed that this property suffices to iteratively build extended formulations of composed polytopes. For the composed polytopes, we show that an extended formulation of the type defined by Margot is always possible only if the smaller polytopes have the projected faces property. Therefore, this produces a characterization of the projected faces property. Affinely generated polyhedral relations were introduced by Kaibel and Pashkovich (Optima 85:2–7, 2011) to construct extended formulations for the convex hull of the images of a point under the action of some finite group of reflections. In this paper we prove that the projected faces property and affinely generated polyhedral relation are equivalent conditions.

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Acknowledgments

We thank the referees for their comments and suggestions, which increased the readability of the present paper.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università degli Studi di Padova, Via Trieste 63, 35121, Padova, Italy

    Michele Conforti

  2. Département de Mathématique, Université libre de Bruxelles, Boulevard du Triomphe, 1050, Brussels, Belgium

    Kanstantsin Pashkovich

Authors
  1. Michele Conforti
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  2. Kanstantsin Pashkovich
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Correspondence to Kanstantsin Pashkovich.

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Supported by “Progetto di Eccellenza 2008–2009” of “Fondazione Cassa di Risparmio di Padova e Rovigo” and Fonds de la Recherche Scientifique de Belgique (FRS-FNRS).

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Conforti, M., Pashkovich, K. The projected faces property and polyhedral relations. Math. Program. 156, 331–342 (2016). https://doi.org/10.1007/s10107-015-0882-5

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  • DOI: https://doi.org/10.1007/s10107-015-0882-5

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