On Ekeland's variational principle for interval-valued functions with applications
Optimization and Control
2021-05-12 v1 Functional Analysis
Abstract
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.
Keywords
Cite
@article{arxiv.2105.04744,
title = {On Ekeland's variational principle for interval-valued functions with applications},
author = {Chuang-liang Zhang and Nan-jing Huang},
journal= {arXiv preprint arXiv:2105.04744},
year = {2021}
}