Remarks on the Monge-Kantorovich problem in the discrete setting

被引：13
|
作者：
Brezis, Haim [1 ,2 ,3 ,4 ]
机构：
[1] Rutgers State Univ, Hill Ctr, Dept Math, Busch Campus,110 Frelinghuysen Rd, Piscataway, NJ 08854 USA
[2] Technion Israel Inst Technol, Dept Math, IL-32000 Haifa, Israel
[3] Technion Israel Inst Technol, Dept Comp Sci, IL-32000 Haifa, Israel
[4] Univ Paris 06, Lab Jacques Louis Lions, 4 Pl Jussieu, F-75252 Paris 05, France
来源：
COMPTES RENDUS MATHEMATIQUE | 2018年 / 356卷 / 02期
关键词：
MONOTONICITY;
D O I：
10.1016/j.crma.2017.12.008
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In Optimal Transport theory, three quantities play a central role: the minimal cost of transport, originally introduced by Monge, its relaxed version introduced by Kantorovich, and a dual formulation also due to Kantorovich. The goal of this Note is to publicize a very elementary, self-contained argument extracted from [9], which shows that all three quantities coincide in the discrete case. (C) 2017 Academie des sciences. Published by Elsevier Masson SAS.
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页码：207 / 213
页数：7
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