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Journal of Convex Analysis 29 (2022), No. 1, 001--012
Copyright Heldermann Verlag 2022

A Simple Relaxation Approach to Duality for Optimal Transport Problems in Completely Regular Spaces

Giuseppe Savaré
Department of Decision Sciences, Bocconi University, Milan, Italy

Giacomo E. Sodini
Fakultät für Mathematik, Technische Universität München, Garching bei München, Germany

We present a simple and direct approach to duality for Optimal Transport for lower semicontinuous cost functionals in arbitrary completely regular topological spaces, showing that the Optimal Transport functional can be interpreted as the largest sublinear and weakly lower semicontinuous functional extending the cost between pairs of Dirac masses.

Keywords: Optimal transport, convex duality, Legendre transform, Fenchel-Moreau theorem.

MSC: 49Q22, 2020, 49N15, 28A33.

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