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