Generalized-Hukuhara Subdifferential Analysis and Its Application in Nonconvex Composite Optimization Problems with Interval-valued Functions
Abstract
In this article, we study -subdifferential calculus of convex interval-valued functions (IVFs) and apply it in a nonconvex composite model of interval optimization problems (IOPs). It is found that the -directional derivative of maximum of finitely many comparable IVFs is the maximum of their -directional derivative. Proposed concepts of -subdifferential are observed to be useful to derive Fritz-John-type and KKT-type efficiency conditions for weak efficient solutions of IOPs. Further, we extract a necessary and sufficient condition to characterize the weak efficient solutions of nonconvex composite IOPs by applying the proposed concepts. To derive the results on -subdifferentials, the concepts of limit supremum and limit infimum with certain properties for IVFs are defined in the sequel. The whole analysis is supported by appropriate expository examples.
Cite
@article{arxiv.2109.14586,
title = {Generalized-Hukuhara Subdifferential Analysis and Its Application in Nonconvex Composite Optimization Problems with Interval-valued Functions},
author = {Anshika and Debdas Ghosh and Ram Surat Chauhan and Radko Mesiar},
journal= {arXiv preprint arXiv:2109.14586},
year = {2021}
}