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On optimality of c-cyclically monotone transference plans

TitleOn optimality of c-cyclically monotone transference plans
Publication TypeJournal Article
Year of Publication2010
AuthorsBianchini, S, Caravenna, L
JournalComptes Rendus Mathematique 348 (2010) 613-618

Abstract. 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 [7]. We emphasize the measurability assumption on the hidden structure of linear preorder, applied also to extremality and uniqueness problems. Resume. Dans la presente note nous decrivons brievement la construction introduite dans [7] a propos de l\\\'equivalence entre l\\\'optimalite d\\\'un plan de transport pour le probleme de Monge-Kantorovich et la condition de monotonie c-cyclique ainsi que d\\\'autres sujets que cela nous amene a aborder. Nous souhaitons mettre en evidence l\\\'hypothese de mesurabilite sur la structure sous-jacente de pre-ordre lineaire.

Alternate JournalSur l\\\'optimalité des plans de transport c-cycliques monotones

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