Emergent Mind
Computing Brascamp-Lieb Constants through the lens of Thompson Geometry
(2208.05013)
Published Aug 9, 2022
in
math.OC
,
cs.CC
,
cs.DS
,
and
math.FA
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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