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UNIVERSAL BOUNDS FOR FIXED POINT ITERATIONS VIA OPTIMAL TRANSPORT METRICS.
- 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