PreprintCC BY 4.0arXiv
Global regularity and sparsity for regularised optimal transport
Abstract
We study regularised optimal transport with subquadratic or entropic regularisation. Under C1,α-assumptions on the marginals and the domains of their support, we prove global gradient-Lipschitz bounds on the potentials, uniform in the regularisation parameter. Moreover, we show that, up to the boundary, the support of the conditional supports supp πε(·|x) behaves like balls of radius ε/ 4 d(p−1)+2. Our work was carried out concurrently and independently of [9]. We obtain the results of [9,Theorem 1.2] under weaker assumptions and with a different proof.
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BibTeX
@misc{cheng2026global,
title = {{Global regularity and sparsity for regularised optimal transport}},
author = {Xiaopeng Cheng and Lukas Koch and Haotian Xiao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01928},
eprint = {2610.01928},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01928},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Global regularity and sparsity for regularised optimal transport
AU - Xiaopeng Cheng
AU - Lukas Koch
AU - Haotian Xiao
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.01928
UR - https://arxiv.org/abs/2610.01928
AB - We study regularised optimal transport with subquadratic or entropic regularisation. Under C^1,α-assumptions on the marginals and the domains of their support, we prove global gradient-Lipschitz bounds on the potentials, uniform in the regularisation parameter. Moreover, we show that, up to the boundary, the support of the conditional supports supp π_ε(·|x) behaves like balls of radius ε^/ 4 d(p−1)+2. Our work was carried out concurrently and independently of [9]. We obtain the results of [9,Theorem 1.2] under weaker assumptions and with a different proof.
ER -