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Ellipsoidal mixed-integer representability

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Abstract

Representability results for mixed-integer linear systems play a fundamental role in optimization since they give geometric characterizations of the feasible sets that can be formulated by mixed-integer linear programming. We consider a natural extension of mixed-integer linear systems obtained by adding just one ellipsoidal inequality. The set of points that can be described, possibly using additional variables, by these systems are called ellipsoidal mixed-integer representable. In this work, we give geometric conditions that characterize ellipsoidal mixed-integer representable sets.

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Authors and Affiliations

  1. Department of Industrial and Systems Engineering, Wisconsin Institute for Discovery, University of Wisconsin-Madison, Madison, WI, USA

    Alberto Del Pia

  2. Department of Mathematics, University of Wisconsin-Madison, Madison, WI, USA

    Jeffrey Poskin

Authors
  1. Alberto Del Pia
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  2. Jeffrey Poskin
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Correspondence to Jeffrey Poskin.

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Del Pia, A., Poskin, J. Ellipsoidal mixed-integer representability. Math. Program. 172, 351–369 (2018). https://doi.org/10.1007/s10107-017-1196-6

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  • DOI: https://doi.org/10.1007/s10107-017-1196-6

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