On the equivalence of static and dynamic weak optimal transport
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866911531031068672 |
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| author | Bulanyi, Bohdan |
| author_facet | Bulanyi, Bohdan |
| contents | We show that there is a PDE formulation in terms of Fokker-Planck equations for weak optimal transport problems. The main novelty is that we introduce a minimization problem involving Fokker-Planck equations in the extended sense of measure-valued solutions and prove that it is equal to the associated weak transport problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_13872 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the equivalence of static and dynamic weak optimal transport Bulanyi, Bohdan Optimization and Control Analysis of PDEs Probability 49Q22, 28A33, 49J45, 49N15, 49Q20 We show that there is a PDE formulation in terms of Fokker-Planck equations for weak optimal transport problems. The main novelty is that we introduce a minimization problem involving Fokker-Planck equations in the extended sense of measure-valued solutions and prove that it is equal to the associated weak transport problem. |
| title | On the equivalence of static and dynamic weak optimal transport |
| topic | Optimization and Control Analysis of PDEs Probability 49Q22, 28A33, 49J45, 49N15, 49Q20 |
| url | https://arxiv.org/abs/2311.13872 |