Geodesic
A Simple Relaxation Approach to Duality for Optimal Transport Problems in Completely Regular Spaces
Journal of convex analysis, Tome 29 (2022) no. 1, pp. 1-12
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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.
Classification : 49Q22, 2020, 49N15, 28A33
Mots-clés : Optimal transport, convex duality, Legendre transform, Fenchel-Moreau theorem 
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     author = {G. Savar\'e and G. E. Sodini},
     title = {A {Simple} {Relaxation} {Approach} to {Duality} for {Optimal} {Transport} {Problems} in {Completely} {Regular} {Spaces}},
     journal = {Journal of convex analysis},
     pages = {1--12},
     year = {2022},
     volume = {29},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2022_29_1_JCA_2022_29_1_a0/}
}
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G. Savaré; G. E. Sodini. A Simple Relaxation Approach to Duality for Optimal Transport Problems in Completely Regular Spaces. Journal of convex analysis, Tome 29 (2022) no. 1, pp. 1-12. http://geodesic.mathdoc.fr/item/JCA_2022_29_1_JCA_2022_29_1_a0/