Ekeland's Variational Principle for Interval-valued Functions
Abstract
In this paper, we attempt to propose Ekeland's variational principle for interval-valued functions (IVFs). To develop the variational principle, we study the concept of sequence of intervals. In the sequel, the idea of gH-semicontinuity for IVFs is explored. A necessary and sufficient condition for an IVF to be gH-continuous in terms of gH-lower and upper semicontinuity is given. Moreover, we prove a characterization for gH-lower semicontinuity by the level sets of the IVF. With the help of this characterization result, we ensure the existence of a minimum for an extended gH-lower semicontinuous, level-bounded and proper IVF. To find an approximate minima of a gH-lower semicontinuous and gH-Gateaux differentiable IVF, the proposed Ekeland's variational principle is used.
Cite
@article{arxiv.2104.11167,
title = {Ekeland's Variational Principle for Interval-valued Functions},
author = {Gourav Kumar and Debdas Ghosh},
journal= {arXiv preprint arXiv:2104.11167},
year = {2021}
}