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On Approximation Algorithms for Concave Mixed-Integer Quadratic Programming

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Integer Programming and Combinatorial Optimization (IPCO 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9682))

Abstract

We describe an algorithm that finds an \(\epsilon \)-approximate solution to a concave mixed-integer quadratic programming problem. The running time of the proposed algorithm is polynomial in the size of the problem and in \(1/\epsilon \), provided that the number of integer variables and the number of negative eigenvalues of the objective function are fixed. The running time of the proposed algorithm is expected unless \(\mathcal {P}=\mathcal {NP}\).

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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

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  1. Alberto Del Pia
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Correspondence to Alberto Del Pia .

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Editors and Affiliations

  1. Université de Liège, Liège, Belgium

    Quentin Louveaux

  2. Technische Universität Berlin, Berlin, Germany

    Martin Skutella

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Del Pia, A. (2016). On Approximation Algorithms for Concave Mixed-Integer Quadratic Programming. In: Louveaux, Q., Skutella, M. (eds) Integer Programming and Combinatorial Optimization. IPCO 2016. Lecture Notes in Computer Science(), vol 9682. Springer, Cham. https://doi.org/10.1007/978-3-319-33461-5_1

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  • DOI: https://doi.org/10.1007/978-3-319-33461-5_1

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-33461-5

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