BARYCENTERS IN THE WASSERSTEIN SPACE

被引：481

作者：

Agueh, Martial ^{[1
]}

Carlier, Guillaume ^{[2
]}

机构：

[1] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3R4, Canada

[2] Univ Paris 09, CNRS, CEREMADE, UMR 7534, F-75775 Paris 16, France

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2011年 / 43卷 / 02期

基金：

加拿大自然科学与工程研究理事会;

关键词：

optimal transport; Wasserstein space; convexity; duality; MAPS;

D O I：

10.1137/100805741

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we introduce a notion of barycenter in the Wasserstein space which generalizes McCann's interpolation to the case of more than two measures. We provide existence, uniqueness, characterizations, and regularity of the barycenter and relate it to the multimarginal optimal transport problem considered by Gangbo and Swiech in [Comm. Pure Appl. Math., 51 (1998), pp. 23-45]. We also consider some examples and, in particular, rigorously solve the Gaussian case. We finally discuss convexity of functionals in the Wasserstein space.

引用

页码：904 / 924

页数：21

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