Geodesic
Duality for the Kantorovich problem with a fixed barycenter and barycenters of functionals
Funkcionalʹnyj analiz i ego priloženiâ, Tome 58 (2024) no. 2, pp. 5-22 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper is devoted to the study of duality in the linear Kantorovich problem with a fixed barycenter. It is proved that Kantorovich duality holds for general lower semicontinuous cost functions on completely regular spaces. In the course of considering this subject, the question of representation of a continuous linear functional by a Radon measure is raised and solved, provided that the barycenter of the functional is given by a Radon measure. In addition, we consider two new barycentric optimization problems and prove duality results for them.
Mots-clés : barycenter
Keywords: cost function, Kantorovich problem. 
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Konstantin Afonin. Duality for the Kantorovich problem with a fixed barycenter and barycenters of functionals. Funkcionalʹnyj analiz i ego priloženiâ, Tome 58 (2024) no. 2, pp. 5-22. http://geodesic.mathdoc.fr/item/FAA_2024_58_2_a1/

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