# Computing Brascamp-Lieb Constants through the lens of Thompson Geometry

arXiv: https://arxiv.org/abs/2208.05013 · HTML: https://mlsanity.com/paper/2208.05013/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Aug 2022.

## Built on by (most cited first, 2 of 2)

- [Disciplined Geodesically Convex Programming](https://mlsanity.com/paper/2407.05261/) (2024)
- [Structured Regularization for Constrained Optimization on the SPD Manifold](https://mlsanity.com/paper/2410.09660/) (2024)

## Abstract (arXiv)

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.