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Extensions on ellipsoid bounds for quadratic integer programming

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Abstract

Ellipsoid bounds for strictly convex quadratic integer programs have been proposed in the literature. The idea is to underestimate the strictly convex quadratic objective function q of the problem by another convex quadratic function with the same continuous minimizer as q and for which an integer minimizer can be easily computed. We initially propose in this paper a different way of constructing the quadratic underestimator for the same problem and then extend the idea to other quadratic integer problems, where the objective function is convex (not strictly convex), and where the objective function is nonconvex and box constraints are introduced. The quality of the bounds proposed is evaluated experimentally and compared to the related existing methodologies.

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Acknowledgements

M. Fampa was partially supported by CNPq Grant 303898/2016-0. F. Pinillos Nieto was supported by a scholarship from CNPq-Brasília-Brazil while developing this work as part of his Ph.D. thesis at the Federal University of Rio de Janeiro. The authors are grateful to Dr. C. Buchheim for valuable clarifications on his papers. The authors also thank the two anonymous referees for their insightful comments and suggestions.

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  1. Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil

    Marcia Fampa & Francisco Pinillos Nieto

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  1. Marcia Fampa
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  2. Francisco Pinillos Nieto
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Correspondence to Marcia Fampa.

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Fampa, M., Nieto, F.P. Extensions on ellipsoid bounds for quadratic integer programming. J Glob Optim 71, 457–482 (2018). https://doi.org/10.1007/s10898-017-0557-2

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