On the Metric Resolvent: Nonexpansiveness, Convergence Rates and Applications On the Metric Resolvent: Nonexpansiveness, Convergence Rates and Applications

In this paper, we study the nonexpansive properties of metric resolvent and present the convergence analysis for the associated fixed-point iterations of both Banach–Picard and Krasnosel’skiĭ–Mann types. A by-product of our expositions also extends the proximity operator and Moreau’s decomposition i...

Full description

Saved in:
Bibliographic Details
Published in:Journal of the Operations Research Society of China (Internet) Vol. 13; no. 4; pp. 966 - 988
Main Author: Xue, Feng
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2025
Springer Nature B.V
Subjects:
Algorithms
Convergence
Convex analysis
Decomposition
Management Science
Mathematics
Mathematics and Statistics
Operations Research
90C25
Metric resolvent
Convergence rates
Operator splitting algorithms
49M29
49M27
47H05
Nonexpansiveness
ISSN:2194-668X, 2194-6698
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, we study the nonexpansive properties of metric resolvent and present the convergence analysis for the associated fixed-point iterations of both Banach–Picard and Krasnosel’skiĭ–Mann types. A by-product of our expositions also extends the proximity operator and Moreau’s decomposition identity to arbitrary metric. It is further shown that many classes of the first-order operator splitting algorithms, including the alternating direction methods of multipliers, primal–dual hybrid gradient and Bregman iterations, can be expressed by the fixed-point iterations of a simple metric resolvent, and thus, the convergence can be easily obtained within this unified framework.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:2194-668X
2194-6698
DOI:10.1007/s40305-023-00518-9