Entropic Approximation of \(\infty \)-Optimal Transport Problems

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2024-06-18 DOI:10.1007/s00245-024-10136-3

Camilla Brizzi, Guillaume Carlier, Luigi De Pascale

引用次数: 0

Abstract

We propose an entropic approximation approach for optimal transportation problems with a supremal cost. We establish \(\Gamma \)-convergence for suitably chosen parameters for the entropic penalization and that this procedure selects \(\infty \)-cyclically monotone plans at the limit. We also present some numerical illustrations performed with Sinkhorn’s algorithm.

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最优传输问题的熵逼近

我们提出了一种熵近似方法来解决具有最高成本的最优运输问题。我们确定了在适当选择熵惩罚参数时的（\Gamma \）收敛性，并且这个过程在极限时选择了（\infty \）循环单调计划。我们还介绍了用辛克霍恩算法进行的一些数值说明。

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

Applied Mathematics and Optimization 数学-应用数学

CiteScore

3.30

自引率

5.60%

发文量

103

审稿时长

>12 weeks

期刊介绍： The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.