Computing Brascamp-Lieb Constants through the lens of Thompson Geometry

Melanie Weber; Suvrit Sra

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arXiv · 2208.05013

Computing Brascamp-Lieb Constants through the lens of Thompson Geometry

Melanie Weber·Suvrit Sra

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Abstract

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.

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BibTeX RIS

Melanie Weber, Suvrit Sra. 2022-08-09. Computing Brascamp-Lieb Constants through the lens of Thompson Geometry. https://arxiv.org/abs/2208.05013

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