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.

翻译：本文研究高效计算Brascamp-Lieb常数的算法，该任务近期受到广泛关注。具体而言，我们将计算问题简化为非线性矩阵值迭代过程，并借助著名的Thompson度量下的不动点方法分析其收敛性。这一方法使我们能够获得（弱）多项式时间保证，并为先前基于黎曼优化与测地凸性的最优方法提供了高效且透明的替代方案。