Transport densities and congested optimal transport problem in the Heisenberg group
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866908615350157312 |
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| author | Circelli, Michele Citti, Giovanna |
| author_facet | Circelli, Michele Citti, Giovanna |
| contents | We adapt the problem of continuous congested optimal transport to the Heisenberg group, equipped with a sub-Riemannian metric. Originally introduced in the Euclidean setting by Carlier, Jimenez, and Santambrogio as a path-dependent variant of the Monge-Kantorovich problem, we significantly restrict the set of admissible curves to horizontal ones. We establish the existence of equilibrium configurations as solutions to a convex minimization problem over a suitable set of measures on horizontal curves. This result is achieved through the notions of horizontal transport density and horizontal traffic intensity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_16052 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Transport densities and congested optimal transport problem in the Heisenberg group Circelli, Michele Citti, Giovanna Optimization and Control We adapt the problem of continuous congested optimal transport to the Heisenberg group, equipped with a sub-Riemannian metric. Originally introduced in the Euclidean setting by Carlier, Jimenez, and Santambrogio as a path-dependent variant of the Monge-Kantorovich problem, we significantly restrict the set of admissible curves to horizontal ones. We establish the existence of equilibrium configurations as solutions to a convex minimization problem over a suitable set of measures on horizontal curves. This result is achieved through the notions of horizontal transport density and horizontal traffic intensity. |
| title | Transport densities and congested optimal transport problem in the Heisenberg group |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2303.16052 |