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Variational Analysis in Cone Pseudo-Quasimetric Spaces and Applications to Group Dynamics

Author

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  • Truong Q. Bao

    (Northern Michigan University)

  • Antoine Soubeyran

    (Aix-Marseille School of Economics, Aix-Marseille University)

Abstract

In this paper, we generalize Ekeland’s variational principle in the new context of cone pseudo-quasimetric spaces. We propose this extension for applications to group dynamics in behavioral sciences. In this setting, a cone pseudo-quasimetric helps to model, in a crude way, multidimensional aspects of resistance to change for a group, where each component represents resistance to change of one agent in the group. At the behavioral level, our new version of Ekeland’s variational principle shows how a group, forming and breaking routines each period by balancing between motivations and resistances to change of all members, can improve step by step their payoffs to end in a trap worthwhile to approach and reach, but not worthwhile to leave.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:170:y:2016:i:2:d:10.1007_s10957-016-0933-y
    DOI: 10.1007/s10957-016-0933-y
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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. Truong Q. Bao & Boris S. Mordukhovich & Antoine Soubeyran, 2015. "Minimal points, variational principles, and variable preferences in set optimization," Post-Print hal-01457319, HAL.
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    Cited by:

    1. 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.
    2. 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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