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Universal bounds for fixed point iterations via optimal transport metrics

Authors :
Champion, Thierry
Bravo, Mario
Cominetti, Roberto
Institut de Mathématiques de Toulon - EA 2134 (IMATH)
Université de Toulon (UTLN)
Publication Year :
2021
Publisher :
arXiv, 2021.

Abstract

We present a self-contained analysis of a particular family of metrics over the set of non-negative 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 very special properties, including their monotonicity and the so-called "convex quadrangle inequality" that yields a greedy algorithm to compute them efficiently.

Details

Database :
OpenAIRE
Accession number :
edsair.doi.dedup.....1d7dfa1345b02b47e9836a2f22928253
Full Text :
https://doi.org/10.48550/arxiv.2108.00300