Equilibrium versions of variational principles in quasi-metric spaces and the robust trap problem. (2nd January 2018)

• Record Type: Journal Article
• Authors: Qiu, Jing-Hui; He, Fei; Soubeyran, Antoine
• Is Part Of: Optimization. Volume 67:Number 1(2018)
• Page Start: 25
• Page End: 53
• Publication Date: 2018-01-02
• Subjects: Pre-order principle -- equilibrium version of Ekeland variational principle -- quasi-metric space -- Caristi's fixed point theorem -- robust trap problem; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2017.1387257
• Languages: English
• ISSNs: 0233-1934

Abstract

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.