WEAK OPTIMAL TRANSPORT WITH UNNORMALIZED KERNELS

Philippe Chone; Nathael Gozlan; Francis Kramarz

doi:10.1137/22M1501301

WEAK OPTIMAL TRANSPORT WITH UNNORMALIZED KERNELS

Philippe Chone
, Nathael Gozlan
, Francis Kramarz

Centre national de la recherche scientifique
Institut Polytechnique de Paris
Uppsala University

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

2 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	6039-6092
Number of pages	54
Journal	SIAM Journal on Mathematical Analysis
Volume	55
Issue number	6
DOIs	https://doi.org/10.1137/22M1501301
Publication status	Published - 1 Dec 2023

Keywords

Strassen's theorem
convex order
duality
optimal transport
weak optimal transport

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10.1137/22M1501301

Cite this

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abstract = "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.",

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author = "Philippe Chone and Nathael Gozlan and Francis Kramarz",

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AU - Kramarz, Francis

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N2 - 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.

AB - 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.

KW - Strassen's theorem

KW - convex order

KW - duality

KW - optimal transport

KW - weak optimal transport

U2 - 10.1137/22M1501301

DO - 10.1137/22M1501301

M3 - Article

AN - SCOPUS:85176811466

SN - 0036-1410

VL - 55

SP - 6039

EP - 6092

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 6

ER -

WEAK OPTIMAL TRANSPORT WITH UNNORMALIZED KERNELS

Abstract

Keywords

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