Quantitative Stability of the Pushforward Operation by an Optimal Transport Map
Optimization and Control
2024-01-08 v2
Abstract
We study the quantitative stability of the mapping that to a measure associates its pushforward measure by a fixed (non-smooth) optimal transport map. We exhibit a tight H\"older-behavior for this operation under minimal assumptions. Our proof essentially relies on a new bound that quantifies the size of the singular sets of a convex and Lipschitz continuous function on a bounded domain.
Cite
@article{arxiv.2401.01088,
title = {Quantitative Stability of the Pushforward Operation by an Optimal Transport Map},
author = {Guillaume Carlier and Alex Delalande and Quentin Mérigot},
journal= {arXiv preprint arXiv:2401.01088},
year = {2024}
}