Directional openness for epigraphical mappings and optimality conditions for directional efficiency. (1st February 2021)

• Record Type: Journal Article
• Authors: Florea, Elena-Andreea; Maxim, Diana
• Is Part Of: Optimization. Volume 70:Number 2(2021)
• Page Start: 321
• Page End: 344
• Publication Date: 2021-02-01
• Subjects: Directional efficiency -- optimality conditions -- directional openness -- epigraphical mappings; 26E25 -- 46G05 -- 90C46; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1711085
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, we consider some notions of directional efficiency in set-valued optimization and we give necessary optimality conditions in primal and dual spaces. The methods we employ are those of variational analysis and generalized differentiation. Auxiliary results relate to the openness of epigraphical set-valued maps under weak assumptions concerning the closedness of the graphs and an appropriate version of the Ekeland Variational Principle.