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Variational rationality, variational principles and the existence of traps in a changing environment

Author

Listed:
  • Majid Fakhar

    (University of Isfahan)

  • Mohammadreza Khodakhah

    (University of Isfahan)

  • Ali Mazyaki

    (Allameh Tabataba’i University)

  • Antoine Soubeyran

    (Aix-Marseille University (Aix-Marseille School of Economics) CNRS EHESS)

  • Jafar Zafarani

    (University of Isfahan)

Abstract

This paper has two aspects. Mathematically, in the context of global optimization, it provides the existence of an optimum of a perturbed optimization problem that generalizes the celebrated Ekeland variational principle and equivalent formulations (Caristi, Takahashi), whenever the perturbations need not satisfy the triangle inequality. Behaviorally, it is a continuation of the recent variational rationality approach of stay (stop) and change (go) human dynamics. It gives sufficient conditions for the existence of traps in a changing environment. In this way it emphasizes even more the striking correspondence between variational analysis in mathematics and variational rationality in psychology and behavioral sciences.

Suggested Citation

  • Majid Fakhar & Mohammadreza Khodakhah & Ali Mazyaki & Antoine Soubeyran & Jafar Zafarani, 2022. "Variational rationality, variational principles and the existence of traps in a changing environment," Journal of Global Optimization, Springer, vol. 82(1), pages 161-177, January.
    • Handle: RePEc:spr:jglopt:v:82:y:2022:i:1:d:10.1007_s10898-021-01061-8
    DOI: 10.1007/s10898-021-01061-8
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    References listed on IDEAS

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    1. T. Q. Bao & B. S. Mordukhovich & A. Soubeyran, 2015. "Variational Analysis in Psychological Modeling," Journal of Optimization Theory and Applications, Springer, vol. 164(1), pages 290-315, January.
    2. Boris S. Mordukhovich & Antoine Soubeyran, 2019. "Variational Analysis and Variational Rationality in Behavioral Sciences: Stationary Traps," Post-Print hal-02096999, HAL.
    3. Truong Q. Bao & Antoine Soubeyran, 2016. "Variational Analysis in Cone Pseudo-Quasimetric Spaces and Applications to Group Dynamics," Journal of Optimization Theory and Applications, Springer, vol. 170(2), pages 458-475, August.
    4. Boris Mordukhovich & Antoine Soubeyran, 2019. "Variational analysis and Variational rationality in Behavioral sciences: stationary traps," Post-Print hal-02084636, HAL.
    5. J. X. Cruz Neto & P. R. Oliveira & A. Soubeyran & J. C. O. Souza, 2020. "A generalized proximal linearized algorithm for DC functions with application to the optimal size of the firm problem," Annals of Operations Research, Springer, vol. 289(2), pages 313-339, June.
    6. T. Q. Bao & S. Cobzaş & A. Soubeyran, 2018. "Variational principles, completeness and the existence of traps in behavioral sciences," Annals of Operations Research, Springer, vol. 269(1), pages 53-79, October.
    7. L. P. Hai & L. Huerga & P. Q. Khanh & V. Novo, 2019. "Variants of the Ekeland variational principle for approximate proper solutions of vector equilibrium problems," Journal of Global Optimization, Springer, vol. 74(2), pages 361-382, June.
    8. Fabián Flores-Bazán & Dinh The Luc & Antoine Soubeyran, 2012. "Maximal Elements Under Reference-Dependent Preferences with Applications to Behavioral Traps and Games," Journal of Optimization Theory and Applications, Springer, vol. 155(3), pages 883-901, December.
    9. Guang-Ya Chen & X. Yang & Hui Yu, 2008. "Vector Ekeland’s variational principle in an F-type topological space," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(3), pages 471-478, June.
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    Cited by:

    1. Le Phuoc Hai & Phan Quoc Khanh & Antoine Soubeyran, 2022. "General Versions of the Ekeland Variational Principle: Ekeland Points and Stop and Go Dynamics," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 347-373, October.

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