On optimality of <i>c</i>-cyclically monotone transference plans

Stefano Bianchini; Laura Caravenna

doi:10.1016/j.crma.2010.03.022

Mathematical Analysis/Calculus of Variations

On optimality of c-cyclically monotone transference plans

Presented by: Michel Talagrand

Stefano Bianchini ¹; Laura Caravenna ²

¹ SISSA, via Beirut 2, 34014 Trieste, Italy
² CRM De Giorgi, Collegio Puteano, Scuola Normale Superiore, Piazza dei Cavalieri 3, 56100 Pisa, Italy

Comptes Rendus. Mathématique, Volume 348 (2010) no. 11-12, pp. 613-618.

Abstract
Résumé

This Note deals with the equivalence between the optimality of a transport plan for the Monge–Kantorovich problem and the condition of c-cyclical monotonicity, as an outcome of the construction in Bianchini and Caravenna (2009) [7]. We emphasize the measurability assumption on the hidden structure of linear preorder, applied also to extremality and uniqueness problems among the family of transport plans.

Dans la présente note nous décrivons brièvement la construction introduite dans Bianchini and Caravenna (2009) [7] à propos de l'équivalence entre l'optimalité d'un plan de transport pour le problème de Monge–Kantorovich et la condition de monotonie c-cyclique—ainsi que d'autres sujets que cela nous amène à aborder. Nous souhaitons mettre en évidence l'hypothèse de mesurabilité sur la structure sous-jacente de pré-ordre linéaire.

Received: 2010-02-04
Accepted: 2010-03-09
Published online: 2010-05-13

DOI: 10.1016/j.crma.2010.03.022

Author's affiliations:

Stefano Bianchini ¹; Laura Caravenna ²

¹ SISSA, via Beirut 2, 34014 Trieste, Italy
² CRM De Giorgi, Collegio Puteano, Scuola Normale Superiore, Piazza dei Cavalieri 3, 56100 Pisa, Italy

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     author = {Stefano Bianchini and Laura Caravenna},
     title = {On optimality of \protect\emph{c}-cyclically monotone transference plans},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {613--618},
     publisher = {Elsevier},
     volume = {348},
     number = {11-12},
     year = {2010},
     doi = {10.1016/j.crma.2010.03.022},
     language = {en},
}

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Stefano Bianchini; Laura Caravenna. On optimality of c-cyclically monotone transference plans. Comptes Rendus. Mathématique, Volume 348 (2010) no. 11-12, pp. 613-618. doi : 10.1016/j.crma.2010.03.022. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.03.022/

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