WEAK OPTIMAL TRANSPORT WITH UNNORMALIZED KERNELS

被引：2

作者：

Chone, Philippe ^{[1
]}

Gozlan, Nathael ^{[2
]}

Kramarz, Francis ^{[3
,4
]}

机构：

[1] CREST, ENSAE, Inst Polytech Paris, Paris, France

[2] Univ Paris Cite, MAP5, CNRS, F-75006 Paris, France

[3] CREST, Inst Polytech Paris, ENSAE, Paris, France

[4] Uppsala Univ, Dept Econ, Uppsala, Sweden

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2023年 / 55卷 / 06期

基金：

欧洲研究理事会;

关键词：

optimal transport; weak optimal transport; duality; convex order; Strassen's theorem; PROBABILITY-MEASURES; REARRANGEMENT; COSTS;

D O I：

10.1137/22M1501301

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce a new variant of the weak optimal transport problem where mass is distributed from one space to the other through unnormalized kernels. We give sufficient conditions for primal attainment and prove a dual formula for this transport problem. We also obtain dual attainment conditions for some specific cost functions. As a byproduct, we obtain a transport characterization of the stochastic order defined by convex positively 1-homogenous functions, in the spirit of the Strassen theorem for convex domination.

引用

页码：6039 / 6092

页数：54

共 50 条

[41] CHARACTERIZATION OF BARYCENTERS IN THE WASSERSTEIN SPACE BY AVERAGING OPTIMAL TRANSPORT MAPS
Bigot, Jeremie
Klein, Thierry
ESAIM-PROBABILITY AND STATISTICS, 2018, 22 : 35 - 57
[42] Application of Optimal Transport to Exact Zoeppritz Equation AVA Inversion
Huang, Guangtan
Chen, Xiaohong
Luo, Cong
Li, Xiangyang
IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, 2018, 15 (09) : 1337 - 1341
[43] Cortically Based Optimal Transport
Galeotti, Mattia
Citti, Giovanna
Sarti, Alessandro
JOURNAL OF MATHEMATICAL IMAGING AND VISION, 2022, 64 (09) : 1040 - 1057
[44] Optimal Transport for Domain Adaptation
Courty, Nicolas
Flamary, Remi
Tuia, Devis
Rakotomamonjy, Alain
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, 2017, 39 (09) : 1853 - 1865
[45] Hierarchical clustering with optimal transport
Chakraborty, Saptarshi
Paul, Debolina
Das, Swagatam
STATISTICS & PROBABILITY LETTERS, 2020, 163
[46] Autoregressive optimal transport models
Zhu, Changbo
Mueller, Hans-Georg
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY, 2023, 85 (03) : 1012 - 1033
[47] On the Hessian of the optimal transport potential
Valdimarsson, Stefan Ingi
ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE, 2007, 6 (03) : 441 - 456
[48] Quantum optimal transport: an invitation
Trevisan, Dario
BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA, 2025, 18 (01): : 347 - 360
[49] The Optimal Partial Transport Problem
Figalli, Alessio
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2010, 195 (02) : 533 - 560
[50] On the Optimal Transport of Semiclassical Measures
Lorenzo Zanelli
Applied Mathematics & Optimization, 2016, 74 : 325 - 342

← 1 2 3 4 5 →