Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Giacomo E. Sodini

Fakultät für Mathematik, Technische Universität München, Garching bei München, Germany

sodini@ma.tum.de

Keywords

  • Optimal transport
  • convex duality
  • Legendre transform
  • Fenchel-Moreau theorem

Mathematics Subject Classification

49Q22, 2020, 49N15, 28A33

Suggested citation

G. Savaré, G. E. Sodini. “A Simple Relaxation Approach to Duality for Optimal Transport Problems in Completely Regular Spaces.” Journal of Convex Analysis 29 (2022), No. 1, 1–12. https://doi.org/10.68381/jca29001

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Published by Heldermann Verlag, 2022. Rights now held by Banach Press.