Universal bounds for fixed point iterations via optimal transport metrics
Mario Bravo, Thierry Champion, Roberto Cominetti · Applied Set-Valued Analysis and Optimization · 2022
We present a self-contained analysis of a particular family of metrics over the set of nonnegative integers.We show that these metrics, which are defined through a nested sequence of optimal transport problems, provide tight estimates for general Krasnosel'skii-Mann fixed point iterations for non-expansive maps.We also describe some of their special properties, including their monotonicity and the so-called convex quadrangle inequality that yields a greedy algorithm for computing them efficiently.