Optimal transport with constraints: from mirror descent to classical mechanics
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914967302701056 |
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| author | Ibrahim, Abdullahi Adinoyi Muehlebach, Michael De Bacco, Caterina |
| author_facet | Ibrahim, Abdullahi Adinoyi Muehlebach, Michael De Bacco, Caterina |
| contents | Finding optimal trajectories for multiple traffic demands in a congested network is a challenging task. Optimal transport theory is a principled approach that has been used successfully to study various transportation problems. Its usage is limited by the lack of principled and flexible ways to incorporate realistic constraints. We propose a principled physics-based approach to impose constraints flexibly in such optimal transport problems. Constraints are included in mirror descent dynamics using the principle of D'Alembert-Lagrange from classical mechanics. This leads to a sparse, local and linear approximation of the feasible set leading in many cases to closed-form updates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_04727 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Optimal transport with constraints: from mirror descent to classical mechanics Ibrahim, Abdullahi Adinoyi Muehlebach, Michael De Bacco, Caterina Physics and Society Classical Physics Finding optimal trajectories for multiple traffic demands in a congested network is a challenging task. Optimal transport theory is a principled approach that has been used successfully to study various transportation problems. Its usage is limited by the lack of principled and flexible ways to incorporate realistic constraints. We propose a principled physics-based approach to impose constraints flexibly in such optimal transport problems. Constraints are included in mirror descent dynamics using the principle of D'Alembert-Lagrange from classical mechanics. This leads to a sparse, local and linear approximation of the feasible set leading in many cases to closed-form updates. |
| title | Optimal transport with constraints: from mirror descent to classical mechanics |
| topic | Physics and Society Classical Physics |
| url | https://arxiv.org/abs/2309.04727 |