2014/04/28 by Mathias Beiglböck, Beiglböck, Mathias, Claus Griessler +1 · 1 citation
Computer Science · Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations #Optimization and Variational Analysis #Point processes and geometric inequalities #Probability (math.PR) #math.FA #math.PR
paper · pdf · doi:10.48550/arxiv.1404.7054
journal version
openalex publication_date 2014/04/28 · arxiv created 2019/08/09 · arxiv updated 2019/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 to infinite-dimensional linear programming problems. This allows us to strengthen known results in martingale optimal transport and the infinitely marginal case of the optimal transport problem. If the optimization problem can be formulated as a multi-marginal transport problem our contribution is parallel to a recent result of Zaev.