论文标题
通过汤普森几何形状的镜头计算Brascamp-Lieb常数
Computing Brascamp-Lieb Constants through the lens of Thompson Geometry
论文作者
论文摘要
本文研究了有效计算Brascamp-Lieb常数的算法，该任务最近引起了人们的兴趣。特别是，我们将计算减少到非线性基质值迭代，我们通过众所周知的汤普森度量下的定点方法的镜头进行分析。这种方法允许我们获得（弱）多项式时间的保证，并提供了基于Riemannian优化和地球凸性的先前最新方法的有效且透明的替代方案。
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.
