On the equivalence between static and dynamic optimal transport governed by linear control systems

Fuente: arXiv
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Autori principali: Einav, Amit, Jiang, Yue, Mészáros, Alpár R.
Natura: Preprint
Pubblicazione: 2025
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author Einav, Amit
Jiang, Yue
Mészáros, Alpár R.
author_facet Einav, Amit
Jiang, Yue
Mészáros, Alpár R.
contents In this paper we revisit a class of optimal transport problems associated to non-autonomous linear control systems. Building on properties of the cost functions on $\mathbb{R}^{d}\times\mathbb{R}^{d}$ derived from suitable variational problems, we show the equivalence between the static and dynamic versions of the corresponding transport problems. Our analysis is constructive in nature and relies on functional analytic properties of the end-point map and the fine properties of the optimal control functions. These lead to some new quantitative estimates which play a crucial role in our investigation.
format Preprint
id arxiv_https___arxiv_org_abs_2505_17570
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle On the equivalence between static and dynamic optimal transport governed by linear control systems
Einav, Amit
Jiang, Yue
Mészáros, Alpár R.
Optimization and Control
Analysis of PDEs
49Q22, 35Q49, 49J15, 49N80
In this paper we revisit a class of optimal transport problems associated to non-autonomous linear control systems. Building on properties of the cost functions on $\mathbb{R}^{d}\times\mathbb{R}^{d}$ derived from suitable variational problems, we show the equivalence between the static and dynamic versions of the corresponding transport problems. Our analysis is constructive in nature and relies on functional analytic properties of the end-point map and the fine properties of the optimal control functions. These lead to some new quantitative estimates which play a crucial role in our investigation.
title On the equivalence between static and dynamic optimal transport governed by linear control systems
topic Optimization and Control
Analysis of PDEs
49Q22, 35Q49, 49J15, 49N80
url https://arxiv.org/abs/2505.17570