On the equivalence between static and dynamic optimal transport governed by linear control systems
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916754690670592 |
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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 |