Fenchel–Rockafellar theorem in infinite dimensions via generalized relative interiors. (2nd January 2023)

• Record Type: Journal Article
• Authors: Cuong, D. V.; Mordukhovich, B. S.; Nam, N. M.; Sandine, G.
• Is Part Of: Optimization. Volume 72:Number 1(2023)
• Page Start: 135
• Page End: 162
• Publication Date: 2023-01-02
• Subjects: Relative interior -- quasi-relative interior -- intrinsic relative interior -- quasi-regularity -- Fenchel duality; 49J52 -- 49J53 -- 90C31; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2022.2048383
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper we provide further studies of Fenchel duality theory in the general framework of locally convex topological vector (LCTV) spaces. We prove the validity of the Fenchel strong duality under some qualification conditions via generalized relative interiors imposed on the epigraphs and the domains of the functions involved. Our results directly generalize the classical Fenchel–Rockafellar theorem on strong duality from finite dimensions to LCTV spaces.