Work

Generalized-Hukuhara Subdifferential Analysis and Its Application in Nonconvex Composite Optimization Problems with Interval-valued Functions

Year: 2021

Type: preprint

Abstract: In this article, we study $gH$-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 $gH$-directional derivative of maximum of finitely many comparable IVFs is the maximum of their $gH$-directional derivative. Proposed concepts of $gH$-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 $gH$-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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2109.14586

Authors: Anshika, Ghosh, Debdas, Chauhan, Ram Surat, Mesiar, Radko

Institutions: Indian Institute of Technology BHU, Banaras Hindu University, Slovak University of Technology in Bratislava, Palacký University Olomouc

Language: English

Topic: Optimization and Variational Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: Agentúra na Podporu Výskumu a Vývoja

Awards: G170866922, G2348664039, G4997663676, Modelovanie neurčitosti: rozšírenia a zovšeobecnenia niektorých špeciálnych metód a ich aplikácie.

OpenAlex ID: W3203586630

Cites: 19

Cited by: 3

Related to: 10