A dynamical formulation of multi-marginal optimal transport
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915545563004928 |
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| author | Pass, Brendan Shenfeld, Yair |
| author_facet | Pass, Brendan Shenfeld, Yair |
| contents | We present a primal-dual dynamical formulation of the multi-marginal optimal transport problem for (semi-)convex cost functions. Even in the two-marginal setting, this formulation applies to cost functions not covered by the classical dynamical approach of Benamou-Brenier. Our dynamical formulation yields a convex optimization problem, enabling the use of convex optimization tools to find quasi-Monge solutions of the static multi-marginal problem for translation-invariant costs. We illustrate our results numerically with proximal splitting methods. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_22494 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A dynamical formulation of multi-marginal optimal transport Pass, Brendan Shenfeld, Yair Optimization and Control Analysis of PDEs Probability 49Q22, 35F21, 49N15, 90C46 We present a primal-dual dynamical formulation of the multi-marginal optimal transport problem for (semi-)convex cost functions. Even in the two-marginal setting, this formulation applies to cost functions not covered by the classical dynamical approach of Benamou-Brenier. Our dynamical formulation yields a convex optimization problem, enabling the use of convex optimization tools to find quasi-Monge solutions of the static multi-marginal problem for translation-invariant costs. We illustrate our results numerically with proximal splitting methods. |
| title | A dynamical formulation of multi-marginal optimal transport |
| topic | Optimization and Control Analysis of PDEs Probability 49Q22, 35F21, 49N15, 90C46 |
| url | https://arxiv.org/abs/2509.22494 |