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First order rejection tests for multiple-objective optimization

Author

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  • Alexandre Goldsztejn
  • Ferenc Domes
  • Brice Chevalier

Abstract

Three rejection tests for multi-objective optimization problems based on first order optimality conditions are proposed. These tests can certify that a box does not contain any local minimizer, and thus it can be excluded from the search process. They generalize previously proposed rejection tests in several regards: Their scope include inequality and equality constrained smooth or nonsmooth multiple objective problems. Reported experiments show that they allow quite efficiently removing the cluster effect in mono-objective and multi-objective problems, which is one of the key issues in continuous global deterministic optimization. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Alexandre Goldsztejn & Ferenc Domes & Brice Chevalier, 2014. "First order rejection tests for multiple-objective optimization," Journal of Global Optimization, Springer, vol. 58(4), pages 653-672, April.
    • Handle: RePEc:spr:jglopt:v:58:y:2014:i:4:p:653-672
    DOI: 10.1007/s10898-013-0066-x
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    References listed on IDEAS

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    1. Xuan-Ha Vu & Hermann Schichl & Djamila Sam-Haroud, 2009. "Interval propagation and search on directed acyclic graphs for numerical constraint solving," Computational Optimization and Applications, Springer, vol. 45(4), pages 499-531, December.
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    Cited by:

    1. Ignacio Araya & Damir Aliquintui & Franco Ardiles & Braulio Lobo, 2021. "Nonlinear biobjective optimization: improving the upper envelope using feasible line segments," Journal of Global Optimization, Springer, vol. 79(2), pages 503-520, February.
    2. Charles Audet & Frédéric Messine & Jordan Ninin, 2022. "Numerical certification of Pareto optimality for biobjective nonlinear problems," Journal of Global Optimization, Springer, vol. 83(4), pages 891-908, August.
    3. Martin, Benjamin & Goldsztejn, Alexandre & Granvilliers, Laurent & Jermann, Christophe, 2017. "Constraint propagation using dominance in interval Branch & Bound for nonlinear biobjective optimization," European Journal of Operational Research, Elsevier, vol. 260(3), pages 934-948.
    4. Tiago Montanher & Arnold Neumaier & Ferenc Domes, 2018. "A computational study of global optimization solvers on two trust region subproblems," Journal of Global Optimization, Springer, vol. 71(4), pages 915-934, August.
    5. Ignacio Araya & Jose Campusano & Damir Aliquintui, 2019. "Nonlinear biobjective optimization: improvements to interval branch & bound algorithms," Journal of Global Optimization, Springer, vol. 75(1), pages 91-110, September.
    6. Rohit Kannan & Paul I. Barton, 2017. "The cluster problem in constrained global optimization," Journal of Global Optimization, Springer, vol. 69(3), pages 629-676, November.
    7. Marendet, Antoine & Goldsztejn, Alexandre & Chabert, Gilles & Jermann, Christophe, 2020. "A standard branch-and-bound approach for nonlinear semi-infinite problems," European Journal of Operational Research, Elsevier, vol. 282(2), pages 438-452.

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