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General Versions of the Ekeland Variational Principle: Ekeland Points and Stop and Go Dynamics

Author

Listed:
  • Le Phuoc Hai

    (HCMUS - Ho Chi Minh City University of Science [Vietnam National University, HCM])

  • Phan Quoc Khanh

    (Ton Duc Thang University [Hô-Chi-Minh-City])

  • Antoine Soubeyran

    (AMSE - Aix-Marseille Sciences Economiques - 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

We establish general versions of the Ekeland variational principle (EVP), where we include two perturbation bifunctions to discuss and obtain better perturbations for obtaining three improved versions of the principle. Here, unlike the usual studies and applications of the EVP, which aim at exact minimizers via a limiting process, our versions provide good-enough approximate minimizers aiming at applications in particular situations. For the presentation of applications chosen in this paper, the underlying space is a partial quasi-metric one. To prove the aforementioned versions, we need a new proof technique. The novelties of the results are in both theoretical and application aspects. In particular, for applications, using our versions of the EVP together with new concepts of Ekeland points and stop and go dynamics, we study in detail human dynamics in terms of a psychological traveler problem, a typical model in behavioral sciences.

Suggested Citation

  • Le Phuoc Hai & Phan Quoc Khanh & Antoine Soubeyran, 2022. "General Versions of the Ekeland Variational Principle: Ekeland Points and Stop and Go Dynamics," Post-Print hal-03784715, HAL.
    • Handle: RePEc:hal:journl:hal-03784715
    DOI: 10.1007/s10957-022-02087-y
    Note: View the original document on HAL open archive server: https://amu.hal.science/hal-03784715v1
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    2. Antoine Soubeyran, 2022. "Variational rationality. Self regulation success as a succession of worthwhile moves that make sufficient progress," Working Papers hal-04041238, HAL.

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