Sponsor
This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.02-2020.20. Research of this author was partly supported by the USA National Science Foundation (Division of Mathematical Sciences) under grants DMS-1512846 and DMS-1808978, by the USA Air Force Office of Scientific Research grant #15RT04, and by Australian Research Council under grant DP-190100555.
Published In
Optimization
Document Type
Pre-Print
Publication Date
3-12-2022
Subjects
Convex geometry, Mathematical optimization, Convex functions, Subdifferentials -- Geometrical aspects
Abstract
In this paper we provide further studies of the 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.
Locate the Document
DOI
10.1080/02331934.2022.2048383
Persistent Identifier
https://archives.pdx.edu/ds/psu/37426
Citation Details
Published as: Cuong, D. V., Mordukhovich, B. S., Nam, N. M., & Sandine, G. (2022). Fenchel–Rockafellar theorem in infinite dimensions via generalized relative interiors. Optimization, 1-28.
Description
This is the author’s version of a work. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document.