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AbsTaylor: upper bounding with inner regions in nonlinear continuous global optimization problems

Author

Listed:
  • Victor Reyes

    (Pontificia Universidad Católica de Valparaíso)

  • Ignacio Araya

    (Pontificia Universidad Católica de Valparaíso)

Abstract

In this paper we propose AbsTaylor, a simple and quick method for extracting inner polytopes, i.e., entirely feasible convex regions in which all points satisfy the constraints. The method performs an inner linearization of the nonlinear constraints by using a Taylor form. Unlike a previous proposal, the expansion point of the Taylor form is not limited to the bounds of the domains, thus producing, in general, a tighter approximation. For testing the approach, AbsTaylor was introduced as an upper bounding method in a state-of-the-art global branch & bound optimizer. Furthermore, we implemented a local search method which extracts feasible inner polytopes for iteratively finding better solutions inside them. In the studied instances, the new method finds in average four times more inner regions and significantly improves the optimizer performance.

Suggested Citation

  • Victor Reyes & Ignacio Araya, 2021. "AbsTaylor: upper bounding with inner regions in nonlinear continuous global optimization problems," Journal of Global Optimization, Springer, vol. 79(2), pages 413-429, February.
    • Handle: RePEc:spr:jglopt:v:79:y:2021:i:2:d:10.1007_s10898-020-00878-z
    DOI: 10.1007/s10898-020-00878-z
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    References listed on IDEAS

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    1. Arne Stolbjerg Drud, 1994. "CONOPT—A Large-Scale GRG Code," INFORMS Journal on Computing, INFORMS, vol. 6(2), pages 207-216, May.
    2. Ignacio Araya & Victor Reyes, 2016. "Interval Branch-and-Bound algorithms for optimization and constraint satisfaction: a survey and prospects," Journal of Global Optimization, Springer, vol. 65(4), pages 837-866, August.
    3. Ignacio Araya & Gilles Trombettoni & Bertrand Neveu & Gilles Chabert, 2014. "Upper bounding in inner regions for global optimization under inequality constraints," Journal of Global Optimization, Springer, vol. 60(2), pages 145-164, October.
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