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A Trust-Region Method for Unconstrained Multiobjective Problems with Applications in Satisficing Processes

Author

Listed:
  • Kelyd.V. Villacorta
  • Paulo R. Oliveira
  • Antoine Soubeyran

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

Abstract

Multiobjective optimization has a significant number of real-life applications. For this reason, in this paper we consider the problem of finding Pareto critical points for unconstrained multiobjective problems and present a trust-region method to solve it. Under certain assumptions, which are derived in a very natural way from assumptions used to establish convergence results of the scalar trust-region method, we prove that our trust-region method generates a sequence which converges in the Pareto critical way. This means that our generalized marginal function, which generalizes the norm of the gradient for the multiobjective case, converges to zero. In the last section of this paper, we give an application to satisficing processes in Behavioral Sciences. Multiobjective trust-region methods appear to be remarkable specimens of much more abstract satisficing processes, based on "variational rationality" concepts. One of their important merits is to allow for efficient computations. This is a striking result in Behavioral Sciences.

Suggested Citation

  • Kelyd.V. Villacorta & Paulo R. Oliveira & Antoine Soubeyran, 2014. "A Trust-Region Method for Unconstrained Multiobjective Problems with Applications in Satisficing Processes," Post-Print hal-01463767, HAL.
    • Handle: RePEc:hal:journl:hal-01463767
    DOI: 10.1007/s10957-013-0392-7
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    Cited by:

    1. Glaydston Carvalho Bento & Gemayqzel Bouza Allende & Yuri Rafael Leite Pereira, 2018. "A Newton-Like Method for Variable Order Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 177(1), pages 201-221, April.
    2. Morovati, Vahid & Pourkarimi, Latif, 2019. "Extension of Zoutendijk method for solving constrained multiobjective optimization problems," European Journal of Operational Research, Elsevier, vol. 273(1), pages 44-57.
    3. Ana Luísa Custódio & Youssef Diouane & Rohollah Garmanjani & Elisa Riccietti, 2021. "Worst-Case Complexity Bounds of Directional Direct-Search Methods for Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 188(1), pages 73-93, January.
    4. A. Mohammadi & A. L. Custódio, 2024. "A trust-region approach for computing Pareto fronts in multiobjective optimization," Computational Optimization and Applications, Springer, vol. 87(1), pages 149-179, January.
    5. N. Eslami & B. Najafi & S. M. Vaezpour, 2023. "A Trust Region Method for Solving Multicriteria Optimization Problems on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 196(1), pages 212-239, January.
    6. Vahid Morovati & Hadi Basirzadeh & Latif Pourkarimi, 2018. "Quasi-Newton methods for multiobjective optimization problems," 4OR, Springer, vol. 16(3), pages 261-294, September.
    7. Nantu Kumar Bisui & Geetanjali Panda, 2025. "A Trust Region Technique for Multiobjective Optimization Problems with Equality and Inequality Constraints," Journal of Optimization Theory and Applications, Springer, vol. 207(1), pages 1-54, October.
    8. S. Liu & L. N. Vicente, 2024. "The stochastic multi-gradient algorithm for multi-objective optimization and its application to supervised machine learning," Annals of Operations Research, Springer, vol. 339(3), pages 1119-1148, August.
    9. Debdas Ghosh, 2025. "Cubic Regularization Technique of the Newton Method for Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 207(2), pages 1-44, November.
    10. Suyun Liu & Luis Nunes Vicente, 2023. "Convergence Rates of the Stochastic Alternating Algorithm for Bi-Objective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 198(1), pages 165-186, July.

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