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arXiv · 2105.04744

On Ekeland's variational principle for interval-valued functions with applications

Chuang-liang Zhang·Nan-jing Huang
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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.

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Chuang-liang Zhang, Nan-jing Huang. 2021-05-11. On Ekeland's variational principle for interval-valued functions with applications. https://arxiv.org/abs/2105.04744

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