UNIVERSAL BOUNDS FOR FIXED POINT ITERATIONS VIA OPTIMAL TRANSPORT METRICS

Mario Bravo; Thierry Champion; Roberto Cominetti

doi:10.23952/asvao.4.2022.3.04

UNIVERSAL BOUNDS FOR FIXED POINT ITERATIONS VIA OPTIMAL TRANSPORT METRICS

Mario Bravo
, Thierry Champion
, Roberto Cominetti

Faculty of Engineering and Science

Research output: Contribution to journal › Article › peer-review

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 special properties, including their monotonicity and the so-called convex quadrangle inequality that yields a greedy algorithm for computing them efficiently.

Original language	English
Pages (from-to)	293-310
Number of pages	18
Journal	Applied Set-Valued Analysis and Optimization
Volume	4
Issue number	3
DOIs	https://doi.org/10.23952/asvao.4.2022.3.04
State	Published - 1 Dec 2022

Keywords

Convergence rates
Error bounds
Fixed-point iterations
Non-expansive maps
Optimal transport metrics

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10.23952/asvao.4.2022.3.04

Cite this

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title = "UNIVERSAL BOUNDS FOR FIXED POINT ITERATIONS VIA OPTIMAL TRANSPORT METRICS",

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{\textquoteright}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",

author = "Mario Bravo and Thierry Champion and Roberto Cominetti",

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N2 - 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 special properties, including their monotonicity and the so-called convex quadrangle inequality that yields a greedy algorithm for computing them efficiently.

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KW - Convergence rates

KW - Error bounds

KW - Fixed-point iterations

KW - Non-expansive maps

KW - Optimal transport metrics

UR - https://www.scopus.com/pages/publications/85135991310

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JO - Applied Set-Valued Analysis and Optimization

JF - Applied Set-Valued Analysis and Optimization

IS - 3

ER -

UNIVERSAL BOUNDS FOR FIXED POINT ITERATIONS VIA OPTIMAL TRANSPORT METRICS

Abstract

Keywords

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