Fenchel-Rockafellar Theorem in Infinite Dimensions via Generalized Relative Interiors
Functional Analysis
2023-03-28 v3 Optimization and Control
Abstract
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.
Keywords
Cite
@article{arxiv.2104.13510,
title = {Fenchel-Rockafellar Theorem in Infinite Dimensions via Generalized Relative Interiors},
author = {Dang Van Cuong and Boris Mordukhovich and Nguyen Mau Nam and Gary Sandine},
journal= {arXiv preprint arXiv:2104.13510},
year = {2023}
}
Comments
arXiv admin note: text overlap with arXiv:1812.00604