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Hybridizing two linear relaxation techniques in interval-based solvers

Author

Listed:
  • Ignacio Araya

    (Pontificia Universidad Católica de Valparaíso)

  • Frédéric Messine

    (University of Toulouse, ENSEEIHT-LAPLACE, CNRS)

  • Jordan Ninin

    (ENSTA-Bretagne, Lab-STICC, team MATRIX)

  • Gilles Trombettoni

    (University of Montpellier, CNRS)

Abstract

In deterministic global optimization, techniques for linear relaxation of a non-convex program are used in the lower bound calculation phase. To achieve this phase, most deterministic global optimization codes use reformulation-linearization techniques. However, there exist also two interval-based polyhedral relaxation techniques which produce reliable bounds without adding new auxiliary variables, and which can take into account mathematical operations and most transcendental functions: (i) the affine relaxation technique, used in the IBBA code, based on affine forms and affine arithmetic, and (ii) the extremal Taylor technique, used in the Ibex-Opt code, which is based on a specific interval-based Taylor form. In this paper, we describe how these two interval-based linear relaxation techniques can be hybridized. These two approaches appear to be complementary, and such a hybrid method performs well on a representative sample of constrained global optimization instances.

Suggested Citation

  • Ignacio Araya & Frédéric Messine & Jordan Ninin & Gilles Trombettoni, 2025. "Hybridizing two linear relaxation techniques in interval-based solvers," Journal of Global Optimization, Springer, vol. 91(3), pages 437-456, March.
    • Handle: RePEc:spr:jglopt:v:91:y:2025:i:3:d:10.1007_s10898-024-01449-2
    DOI: 10.1007/s10898-024-01449-2
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    References listed on IDEAS

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    1. 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.
    2. Ruth Misener & Christodoulos Floudas, 2014. "ANTIGONE: Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Equations," Journal of Global Optimization, Springer, vol. 59(2), pages 503-526, July.
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