A pre-order principle and set-valued Ekeland variational principle

2013/11/20 by Jinghui Qiu, Jing-Hui Qiu, Qiu, Jing-Hui · 1 citation
Computer Science · Mathematics · #46A03 #49J53 #65K10 #90C48 #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Differential Equations Analysis #Optimization and Variational Analysis #math.FA #msc:46A03 #msc:49J53 #msc:65K10 #msc:90C48

paper · pdf · doi:10.48550/arxiv.1311.4951

This paper includes 47 pages

arxiv created 2013/11/20 · openalex publication_date 2013/11/20 · arxiv updated 2013/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish a pre-order principle. From the principle, we obtain a very general set-valued Ekeland variational principle, where the objective function is a set-valued map taking values in a quasi ordered linear space and the perturbation contains a family of set-valued maps satisfying certain property. From this general set-valued Ekeland variational principle, we deduce a number of particular versions of set-valued Ekeland variational principle, which include many known Ekeland variational principles, their improvements and some new results.

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