Computational semi-discrete optimal transport with general storage fees

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:503

Article

Bansil, Mohit¹ 

[1] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90024 USA

关键词: Optimal transport;    Newton method;    Laguerre cell;   

DOI  :  10.1016/j.jmaa.2021.125287

来源: Elsevier

【 摘 要 】

We propose and analyze a modified damped Newton algorithm to solve the semidiscrete optimal transport with storage fees. We prove global linear convergence for a wide range of storage fee functions, the main assumption being that each warehouse's storage costs are independent. We show that if F is an arbitrary storage fee function that satisfies this independence condition then F can be perturbed into a new storage fee function so that our algorithm converges. We also show that the optimizers are stable under these perturbations. Furthermore, our results come with quantitative rates. (C) 2021 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

【 授权许可】

Free