ECM - École Centrale de Marseille : UMR7316 (Pôle de l'étoile - Technopole de Château-Gombert - 38 rue Frédéric Joliot-Curie - 13013 Marseille - France)
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.
https://hal-amu.archives-ouvertes.fr/hal-02084464 Contributor : Elisabeth LhuillierConnect in order to contact the contributor Submitted on : Tuesday, February 1, 2022 - 6:24:45 PM Last modification on : Monday, May 16, 2022 - 12:16:04 PM Long-term archiving on: : Tuesday, May 3, 2022 - 8:49:05 AM
Jing-Hui Qiu, Fei He, Antoine Soubeyran. Equilibrium versions of variational principles in quasi-metric spaces and the robust trap problem. Optimization, Taylor & Francis, 2017, 67 (1), pp.25-53. ⟨10.1080/02331934.2017.1387257⟩. ⟨hal-02084464⟩