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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. Le An & Pham Tao, 2005. "The DC (Difference of Convex Functions) Programming and DCA Revisited with DC Models of Real World Nonconvex Optimization Problems," Annals of Operations Research, Springer, vol. 133(1), pages 23-46, January.
    2. Marcia Fampa & Jon Lee & Wendel Melo, 2017. "On global optimization with indefinite quadratics," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 5(3), pages 309-337, September.
    3. 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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