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.

引用

页码：207 / 213

页数：7

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