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Extensions on ellipsoid bounds for quadratic integer programming

Author

Listed:
  • Marcia Fampa

    (Universidade Federal do Rio de Janeiro)

  • Francisco Pinillos Nieto

    (Universidade Federal do Rio de Janeiro)

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.

Suggested Citation

  • Marcia Fampa & Francisco Pinillos Nieto, 2018. "Extensions on ellipsoid bounds for quadratic integer programming," Journal of Global Optimization, Springer, vol. 71(3), pages 457-482, July.
    • Handle: RePEc:spr:jglopt:v:71:y:2018:i:3:d:10.1007_s10898-017-0557-2
    DOI: 10.1007/s10898-017-0557-2
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    References listed on IDEAS

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    1. R. Horst & N. V. Thoai, 1999. "DC Programming: Overview," Journal of Optimization Theory and Applications, Springer, vol. 103(1), pages 1-43, October.
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