Computing Brascamp-Lieb Constants through the lens of Thompson Geometry

Autor:	Weber, Melanie, Sra, Suvrit
Rok vydání:	2022
Předmět:	Mathematics - Optimization and Control Computer Science - Computational Complexity Computer Science - Data Structures and Algorithms Mathematics - Functional Analysis 46N10 49Q99 53Z50 68W40
Druh dokumentu:	Working Paper
Popis:	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. Comment: Under Review
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2208.05013 Zobrazit plný text záznamu View this record from Arxiv