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Fenchel-Young inequality with a remainder and applications to convex duality and optimal transport

Carlier, Guillaume (2022), Fenchel-Young inequality with a remainder and applications to convex duality and optimal transport. https://basepub.dauphine.psl.eu/handle/123456789/24065

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Type
Document de travail / Working paper
Date
2022
Series title
Cahier de recherche CEREMADE, Université Paris Dauphine-PSL
Published in
Paris
Pages
10
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Author(s)
Carlier, Guillaume
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
This short note is devoted to some applications of a simple quantitative form of the Fenchel-Young inequality in Hilbert spaces. Our initial motivation comes from a stability question in optimal transport. We derive from the quantitative form of the Fenchel-Young inequality a simple and constructive proof of the Brøndsted-Rockafellar theorem and a perturbed primal-dual attainment result in Hilbert spaces.
Subjects / Keywords
Fenchel-Young inequality in quantitative form; Brøndsted-Rockafellar theorem; Tilted convex duality; Stability of optimal transport