Optimal Transport of Maps

Woochul Jung; Carlos Morales; Xiao Wen

doi:10.1007/s10957-024-02576-2

Optimal Transport of Maps

Woochul Jung^*
, Carlos Morales
, Xiao Wen

^*Corresponding author for this work

School of Artificial Intelligence(Institute of Artificial Intelligence)

Konyang University
Beihang University
Beijing Academy of Blockchain and Edge Computing
Zhongguancun Laboratory

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

Abstract

The problem of transporting graphs of continuous maps in a metric space with minimal cost is formulated. The minimal cost distance generated by this problem in the space of continuous maps is studied. The topology induced by this distance will be studied. A measure-theoretical version of the minimal cost distance will be given.

Original language	English
Article number	23
Journal	Journal of Optimization Theory and Applications
Volume	204
Issue number	2
DOIs	https://doi.org/10.1007/s10957-024-02576-2
State	Published - Feb 2025

Keywords

Mapping
Metric space
Optimal transport

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10.1007/s10957-024-02576-2

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title = "Optimal Transport of Maps",

abstract = "The problem of transporting graphs of continuous maps in a metric space with minimal cost is formulated. The minimal cost distance generated by this problem in the space of continuous maps is studied. The topology induced by this distance will be studied. A measure-theoretical version of the minimal cost distance will be given.",

keywords = "Mapping, Metric space, Optimal transport",

author = "Woochul Jung and Carlos Morales and Xiao Wen",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.",

year = "2025",

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doi = "10.1007/s10957-024-02576-2",

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AU - Morales, Carlos

AU - Wen, Xiao

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PY - 2025/2

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N2 - The problem of transporting graphs of continuous maps in a metric space with minimal cost is formulated. The minimal cost distance generated by this problem in the space of continuous maps is studied. The topology induced by this distance will be studied. A measure-theoretical version of the minimal cost distance will be given.

AB - The problem of transporting graphs of continuous maps in a metric space with minimal cost is formulated. The minimal cost distance generated by this problem in the space of continuous maps is studied. The topology induced by this distance will be studied. A measure-theoretical version of the minimal cost distance will be given.

KW - Mapping

KW - Metric space

KW - Optimal transport

UR - https://www.scopus.com/pages/publications/85217824532

U2 - 10.1007/s10957-024-02576-2

DO - 10.1007/s10957-024-02576-2

M3 - 文章

AN - SCOPUS:85217824532

SN - 0022-3239

VL - 204

JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

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Optimal Transport of Maps

Abstract

Keywords

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