Quantitative Stability of the Pushforward Operation by an Optimal Transport Map

IF 2.5 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Foundations of Computational Mathematics Pub Date : 2024-07-19 DOI:10.1007/s10208-024-09669-4

Guillaume Carlier, Alex Delalande, Quentin Mérigot

引用次数: 0

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 Hölder-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.

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通过最优传输图实现前推操作的定量稳定性

我们研究了用固定的（非光滑的）最优传输映射来关联一个度量的前推度量的映射的定量稳定性。在极少假设条件下，我们展示了这一操作的严密荷尔德行为。我们的证明主要依赖于一个新的约束，它量化了有界域上凸函数和利普希兹连续函数奇异集的大小。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Foundations of Computational Mathematics 数学-计算机：理论方法

CiteScore

6.90

自引率

3.30%

发文量

审稿时长

>12 weeks

期刊介绍： Foundations of Computational Mathematics (FoCM) will publish research and survey papers of the highest quality which further the understanding of the connections between mathematics and computation. The journal aims to promote the exploration of all fundamental issues underlying the creative tension among mathematics, computer science and application areas unencumbered by any external criteria such as the pressure for applications. The journal will thus serve an increasingly important and applicable area of mathematics. The journal hopes to further the understanding of the deep relationships between mathematical theory: analysis, topology, geometry and algebra, and the computational processes as they are evolving in tandem with the modern computer. With its distinguished editorial board selecting papers of the highest quality and interest from the international community, FoCM hopes to influence both mathematics and computation. Relevance to applications will not constitute a requirement for the publication of articles. The journal does not accept code for review however authors who have code/data related to the submission should include a weblink to the repository where the data/code is stored.