Equilibrium versions of set-valued variational principles and their applications to organizational behavior. (1st December 2020)

• Record Type: Journal Article
• Authors: Qiu, Jing-Hui; Soubeyran, Antoine; He, Fei
• Is Part Of: Optimization. Volume 69:Number 12(2020)
• Page Start: 2657
• Page End: 2693
• Publication Date: 2020-12-01
• Subjects: Equilibrium version of Ekeland variational principle -- set-valued perturbation -- quasi-metric space -- organizational change -- existence of robust organizational traps; 49J53 -- 90C29; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1718127
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: By 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 function is a set-valued bimap defined on the product of left-complete quasi-metric spaces and taking values in a quasi-ordered linear space, and the perturbation consists of a cone-convex subset of the ordering cone multiplied by the quasi-metric. Moreover, we obtain an equilibrium EVP, where the perturbation contains a σ -convex subset and the quasi-metric. From the above two general EVPs, we deduce several interesting corollaries, which extend and improve the related known results. Several examples show that the obtained set-valued EVPs are new. Finally, applying the above EVPs to organizational behavior sciences, we obtain some interesting results on organizational change and development with leadership. In particular, we show that the existence of robust organizational traps.