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Fenchel-Rockafellar Theorem in Infinite Dimensions via Generalized Relative Interiors

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arxiv 2104.13510 v3 pith:SC7EB3IY submitted 2021-04-27 math.FA math.OC

Dang Van Cuong , Boris Mordukhovich , Nguyen Mau Nam , Gary Sandine This is my paper · ORCID
classification math.FAmath.OC
keywords dualitydimensionsfenchelfenchel-rockafellargeneralizedinteriorslctvrelative
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In this paper we provide further studies of the Fenchel duality theory in the general frame work 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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