[Sur l'optimalité des plans de transport c-cycliques monotones]
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.
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.
Accepté le :
Publié le :
Stefano Bianchini 1 ; Laura Caravenna 2
@article{CRMATH_2010__348_11-12_613_0, 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}, }
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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