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...

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Veröffentlicht in:Journal of the Operations Research Society of China (Internet) Jg. 13; H. 4; S. 966 - 988
1. Verfasser: Xue, Feng
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2025
Springer Nature B.V
Schlagworte:
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
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Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:2194-668X
2194-6698
DOI:10.1007/s40305-023-00518-9