Abstract cyclical monotonicity and Monge solutions for the general Monge-Kantorovich problem

作     者：Levin, V 

作者机构：Russian Acad Sci Cent Econ & Math Inst Moscow 117418 Russia 

出 版 物：《SET-VALUED ANALYSIS》 (集值分析)

年 卷 期：1999年第7卷第1期

页      面：7-32页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：INTAS, (97-1050) Russian Foundation for Basic Research, RFBR, (99-01-00235) 

主　　题：L-cyclical monotonicity L-convex function L-subdifferential multifunction Q(0) general Monge-Kantorovich problem measure preserving map 

摘      要：Abstract cyclical monotonicity is studied for a multivalued operator F : X -- L, where L subset of or equal to 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.