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Journal Articles Optimization Year : 2022

Equilibrium set-valued variational principles and the lower boundedness condition with application to psychology

Abstract

We first give a pre-order principle whose form is very general. Combining the pre-order principle and generalized Gerstewitz functions, 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 quasi-metric spaces and taking values in a quasi-ordered linear space, and the perturbation consists of a subset of the ordering cone multiplied by the quasi-metric. From this, we obtain a number of new results which essentially improve the related results. Particularly, the earlier lower boundedness condition has been weakened. Finally, we apply the new EVPs to Psychology.
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Dates and versions

hal-03784742 , version 1 (23-09-2022)

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Jing-Hui Qiu, Antoine Soubeyran, Fei He. Equilibrium set-valued variational principles and the lower boundedness condition with application to psychology. Optimization, In press, pp.1-33. ⟨10.1080/02331934.2022.2123240⟩. ⟨hal-03784742⟩
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