On the geometry and dynamical formulation of the Sinkhorn algorithm for optimal transport
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866909731615932416 |
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| author | Modin, Klas |
| author_facet | Modin, Klas |
| contents | The Sinkhorn algorithm is a numerical method for the solution of optimal transport problems. Here, I give a brief survey of this algorithm, with a strong emphasis on its geometric origin: it is natural to view it as a discretization, by standard methods, of a non-linear integral equation. In the appendix, I also provide a short summary of an early result of Beurling on product measures, directly related to the Sinkhorn algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_09089 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the geometry and dynamical formulation of the Sinkhorn algorithm for optimal transport Modin, Klas Numerical Analysis Differential Geometry 49Q22, 35Q49, 37K65, 65R20 The Sinkhorn algorithm is a numerical method for the solution of optimal transport problems. Here, I give a brief survey of this algorithm, with a strong emphasis on its geometric origin: it is natural to view it as a discretization, by standard methods, of a non-linear integral equation. In the appendix, I also provide a short summary of an early result of Beurling on product measures, directly related to the Sinkhorn algorithm. |
| title | On the geometry and dynamical formulation of the Sinkhorn algorithm for optimal transport |
| topic | Numerical Analysis Differential Geometry 49Q22, 35Q49, 37K65, 65R20 |
| url | https://arxiv.org/abs/2309.09089 |