M. Beiglböck, C. Griessler:
"A land of monotone plenty";
Annali Della Scuola Normale Superiore di Pisa-Classe di Scienze, June (2017), S. 1 - 17.

Kurzfassung englisch:
A fundamental concept in optimal transport is c-cyclical monotonicity: it allows to link the optimality of transport plans to the geometry of their support sets. Recently, related concepts have been successfully applied in the multi-marginal version of the transport problem as well as in the martingale transport problem which arises from model-independent finance.
We establish a unifying concept of c-monotonicity / finitistic optimality which describes the geometric structure of optimizers of a generalized moment problem. This allows us to strengthen known results in optimal martingale transport and for a transport problem with a continuum of marginals.
If the optimization problem can be formulated as a multi-marginal
transport problem, potentially with additional linear constraints, our contribution is parallel to a recent result of Zaev.

cyclical monotonicity mass transport moment problem / MSC (2010): Primary 60G42, 60G44; Secondary 91G20;

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