2021/05/11 by Chuang-liang Zhang, Nan-jing Huang, Zhang, Chuang-liang +2
Computer Science · Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #Fuzzy Systems and Optimization #Optimization and Control (math.OC) #Optimization and Variational Analysis #math.FA #math.OC
paper · pdf · doi:10.48550/arxiv.2105.04744
arxiv created 2021/05/11 · openalex publication_date 2021/05/11 · arxiv updated 2021/05/12 · openalex created_date 2021/05/24 · openalex updated_date 2026/07/28
In this paper, we obtain a version of Ekeland's variational principle for interval-value functions by means of the Dancs-Hegedus-Medvegyev theorem [14]. We also derive two versions of Ekeland's variational principle involving the generalized Hukuhara Gateaux differentiability of interval-valued functions as well as a version of Ekeland's variational principle for interval-valued bifunctions. Finally, we apply these new versions of Ekeland's variational principle to fixed point theorems, to interval-valued optimization problems, to the interval-valued Mountain Pass Theorem, to noncooperative interval-valued games, and to interval-valued optimal control problems described by interval-valued differential equations.