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UNIVERSAL BOUNDS FOR FIXED POINT ITERATIONS VIA OPTIMAL TRANSPORT METRICS.

Authors :
BRAVO, MARIO
CHAMPION, THIERRY
COMINETTI, ROBERTO
Source :
Applied Set-Valued Analysis & Optimization; 2022, Vol. 4 Issue 3, p293-310, 18p
Publication Year :
2022

Abstract

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. Keywords. Convergence rates; Error bounds; Fixed-point iterations, Non-expansive maps; Optimal transport metrics. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
25627775
Volume :
4
Issue :
3
Database :
Complementary Index
Journal :
Applied Set-Valued Analysis & Optimization
Publication Type :
Academic Journal
Accession number :
159186595
Full Text :
https://doi.org/10.23952/asvao.4.2022.3.04