IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-02084464.html
   My bibliography  Save this paper

Equilibrium versions of variational principles in quasi-metric spaces and the robust trap problem

Author

Listed:
  • Jing-Hui Qiu

    (Soochow University)

  • Fei He

    (THU - Tsinghua University [Beijing])

  • 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

Using a pre-order principle in [Qiu JH. A pre-order principle and set-valued Ekeland variational principle. J Math Anal Appl. 2014;419:904–937], we establish a general equilibrium version of set-valued Ekeland variational principle (denoted by EVP), where the objective bimap is defined on the product of left-complete quasi-metric spaces and taking values in a quasi-order linear space, and the perturbation consists of the quasi-metric and a positive vector . Here, the ordering is only to be -closed, which is strictly weaker than to be topologically closed. From the general equilibrium version, we deduce a number of particular equilibrium versions of EVP with set-valued bimaps or with vector-valued bimap. As applications of the equilibrium versions of EVP, we present several interesting results on equilibrium problems, vector optimization and fixed point theory in the setting of quasi-metric spaces. These results extend and improve the related known results. Using the obtained EVPs, we further study the existence and the robustness of traps in Behavioural Sciences.

Suggested Citation

  • Jing-Hui Qiu & Fei He & Antoine Soubeyran, 2017. "Equilibrium versions of variational principles in quasi-metric spaces and the robust trap problem," Post-Print hal-02084464, HAL.
    • Handle: RePEc:hal:journl:hal-02084464
    DOI: 10.1080/02331934.2017.1387257
    Note: View the original document on HAL open archive server: https://amu.hal.science/hal-02084464
    as

    Download full text from publisher

    File URL: https://amu.hal.science/hal-02084464/document
    Download Restriction: no
    File URL: https://libkey.io/10.1080/02331934.2017.1387257?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Phan Khanh & Dinh Quy, 2013. "Versions of Ekeland’s variational principle involving set perturbations," Journal of Global Optimization, Springer, vol. 57(3), pages 951-968, November.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jing-Hui Qiu & Antoine Soubeyran & Fei He, 2020. "Equilibrium versions of set-valued variational principles and their applications to organizational behavior," Post-Print hal-02465110, HAL.
    2. 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.
    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. Glaydston Carvalho Bento & João Xavier Cruz Neto & Antoine Soubeyran & Valdinês Leite Sousa Júnior, 2016. "Dual Descent Methods as Tension Reduction Systems," Journal of Optimization Theory and Applications, Springer, vol. 171(1), pages 209-227, October.
    5. 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.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:journl:hal-02084464. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.