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.
Convex geometry, Mathematical optimization, Convex functions, Subdifferentials -- Geometrical aspects
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.
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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.