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On approximation algorithms for concave mixed-integer quadratic programming

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Abstract

Concave mixed-integer quadratic programming is the problem of minimizing a concave quadratic polynomial over the mixed-integer points in a polyhedral region. In this work 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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  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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Del Pia, A. On approximation algorithms for concave mixed-integer quadratic programming. Math. Program. 172, 3–16 (2018). https://doi.org/10.1007/s10107-017-1178-8

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