New concepts of directional derivatives for set-valued maps and applications to set optimization. (3rd April 2023)

• Record Type: Journal Article
• Authors: Burlică, Monica; Durea, Marius; Strugariu, Radu
• Is Part Of: Optimization. Volume 72:Number 4(2023)
• Page Start: 1069
• Page End: 1091
• Publication Date: 2023-04-03
• Subjects: Set optimization -- directional derivatives -- optimality conditions; 54C60 -- 46G05 -- 90C46; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2022.2088368
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: We introduce and study two directional derivatives adapted to the case of set optimization. We motivate our approach by the novelty and the flexibility of these constructions for set optimization problems and by their relations, in some particular cases, to known objects of generalized differentiation. We prove optimality conditions for unconstrained problems on the basis of these derivatives and we extend these conditions to constrained problems by means of a penalization result and some calculus rules.