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Abstract Cyclical Monotonicity and Monge Solutions for the General Monge–Kantorovich Problem

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Abstract

Abstract cyclical monotonicity is studied for a multivalued operator F : X → L, where L \( \subseteq\) R X. A criterion for F to be L-cyclically monotone is obtained and connections with the notions of L-convex function and of its L-subdifferentials are established. Applications are given to the general Monge–Kantorovich problem with fixed marginals. In particular, we show that in some cases the optimal measure is unique and generated by a unique (up to the a.e. equivalence) optimal solution (measure preserving map) for the corresponding Monge problem.

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  1. Central Economics and Mathematics Institute of the Russian Academy of Sciences, 47 Nakhimovskii Prospect, 117418, Moscow, Russia

    Vladimir Levin

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Levin, V. Abstract Cyclical Monotonicity and Monge Solutions for the General Monge–Kantorovich Problem. Set-Valued Analysis 7, 7–32 (1999). https://doi.org/10.1023/A:1008753021652

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