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Characterizations of mixed binary convex quadratic representable sets

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Representability results play a fundamental role in optimization since they provide characterizations of the feasible sets that arise from optimization problems. In this paper we study the sets that appear in the feasibility version of mixed binary convex quadratic optimization problems. We provide a complete characterization of the sets that can be obtained as the projection of such feasible regions. In order to obtain this result, we first provide a complete characterization of these sets in the special cases where (1) the feasible region is bounded, (2) only binary extended variables are present, and (3) only continuous variables are present.

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Authors and Affiliations

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

    Alberto Del Pia

  2. Department of Mathematics and Wisconsin Institute for Discovery, University of Wisconsin-Madison, Madison, WI, USA

    Jeffrey Poskin

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

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Del Pia, A., Poskin, J. Characterizations of mixed binary convex quadratic representable sets. Math. Program. 177, 371–394 (2019). https://doi.org/10.1007/s10107-018-1274-4

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  • DOI: https://doi.org/10.1007/s10107-018-1274-4

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