A Duality-Based Proof of the Triangle Inequality for the Wasserstein Distances

François Golse

doi:10.1007/s44007-023-00082-x

A Duality-Based Proof of the Triangle Inequality for the Wasserstein Distances

François Golse

Research output: Contribution to journal › Article › peer-review

Abstract

This short note gives a proof of the triangle inequality based on the Kantorovich duality formula for the Wasserstein distances of exponent p∈[1,+∞) in the case of a general Polish space. In particular, it avoids the “gluing of couplings” procedure used in most textbooks on optimal transport.

Original language	English
Pages (from-to)	196-210
Number of pages	15
Journal	Matematica
Volume	3
Issue number	1
DOIs	https://doi.org/10.1007/s44007-023-00082-x
Publication status	Published - 1 Mar 2024

Keywords

49N15 (60B10)
49Q22
Kantorovich duality
Optimal transport
Triangle inequality
Wasserstein distance

Access to Document

10.1007/s44007-023-00082-x

Cite this

@article{2878b609d61d4a9084be597944a86ea1,

title = "A Duality-Based Proof of the Triangle Inequality for the Wasserstein Distances",

abstract = "This short note gives a proof of the triangle inequality based on the Kantorovich duality formula for the Wasserstein distances of exponent p∈[1,+∞) in the case of a general Polish space. In particular, it avoids the “gluing of couplings” procedure used in most textbooks on optimal transport.",

keywords = "49N15 (60B10), 49Q22, Kantorovich duality, Optimal transport, Triangle inequality, Wasserstein distance",

author = "Fran{\c c}ois Golse",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer Science+Business Media LLC, part of Springer Nature 2024.",

year = "2024",

month = mar,

day = "1",

doi = "10.1007/s44007-023-00082-x",

language = "English",

volume = "3",

pages = "196--210",

journal = "Matematica",

issn = "2730-9657",

number = "1",

}

TY - JOUR

T1 - A Duality-Based Proof of the Triangle Inequality for the Wasserstein Distances

AU - Golse, François

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Science+Business Media LLC, part of Springer Nature 2024.

PY - 2024/3/1

Y1 - 2024/3/1

N2 - This short note gives a proof of the triangle inequality based on the Kantorovich duality formula for the Wasserstein distances of exponent p∈[1,+∞) in the case of a general Polish space. In particular, it avoids the “gluing of couplings” procedure used in most textbooks on optimal transport.

AB - This short note gives a proof of the triangle inequality based on the Kantorovich duality formula for the Wasserstein distances of exponent p∈[1,+∞) in the case of a general Polish space. In particular, it avoids the “gluing of couplings” procedure used in most textbooks on optimal transport.

KW - 49N15 (60B10)

KW - 49Q22

KW - Kantorovich duality

KW - Optimal transport

KW - Triangle inequality

KW - Wasserstein distance

UR - https://www.scopus.com/pages/publications/85195550991

U2 - 10.1007/s44007-023-00082-x

DO - 10.1007/s44007-023-00082-x

M3 - Article

AN - SCOPUS:85195550991

SN - 2730-9657

VL - 3

SP - 196

EP - 210

JO - Matematica

JF - Matematica

IS - 1

ER -

A Duality-Based Proof of the Triangle Inequality for the Wasserstein Distances

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this