Computing Brascamp-Lieb Constants through the lens of Thompson Geometry
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866913312405454848 |
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| author | Weber, Melanie Sra, Suvrit |
| author_facet | Weber, Melanie Sra, Suvrit |
| contents | This paper studies algorithms for efficiently computing Brascamp-Lieb constants, a task that has recently received much interest. In particular, we reduce the computation to a nonlinear matrix-valued iteration, whose convergence we analyze through the lens of fixed-point methods under the well-known Thompson metric. This approach permits us to obtain (weakly) polynomial time guarantees, and it offers an efficient and transparent alternative to previous state-of-the-art approaches based on Riemannian optimization and geodesic convexity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_05013 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Computing Brascamp-Lieb Constants through the lens of Thompson Geometry Weber, Melanie Sra, Suvrit Optimization and Control Computational Complexity Data Structures and Algorithms Functional Analysis 46N10, 49Q99, 53Z50, 68W40 This paper studies algorithms for efficiently computing Brascamp-Lieb constants, a task that has recently received much interest. In particular, we reduce the computation to a nonlinear matrix-valued iteration, whose convergence we analyze through the lens of fixed-point methods under the well-known Thompson metric. This approach permits us to obtain (weakly) polynomial time guarantees, and it offers an efficient and transparent alternative to previous state-of-the-art approaches based on Riemannian optimization and geodesic convexity. |
| title | Computing Brascamp-Lieb Constants through the lens of Thompson Geometry |
| topic | Optimization and Control Computational Complexity Data Structures and Algorithms Functional Analysis 46N10, 49Q99, 53Z50, 68W40 |
| url | https://arxiv.org/abs/2208.05013 |