Quantitative results on a Halpern-type proximal point algorithm

We apply proof mining methods to analyse a result of Boikanyo and Moroşanu on the strong convergence of a Halpern-type proximal point algorithm. As a consequence, we obtain quantitative versions of this result, providing uniform effective rates of asymptotic regularity and metastability.

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Bibliographic Details
Published in:Computational optimization and applications Vol. 79; no. 1; pp. 101 - 125
Main Authors: Leuştean, Laurenţiu, Pinto, Pedro
Format: Journal Article
Language:English
Published: New York Springer US 01.05.2021
Springer Nature B.V
Subjects:
Algorithms
Convex and Discrete Geometry
Management Science
Mathematics
Mathematics and Statistics
Operations Research
Operations Research/Decision Theory
Optimization
Statistics
Rates of convergence
Rates of metastability
Proof mining
Maximally monotone operators
Halpern iteration
47H09
Proximal point algorithm
47H05
47J25
03F10
ISSN:0926-6003, 1573-2894
Online Access:Get full text
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Description
Summary:We apply proof mining methods to analyse a result of Boikanyo and Moroşanu on the strong convergence of a Halpern-type proximal point algorithm. As a consequence, we obtain quantitative versions of this result, providing uniform effective rates of asymptotic regularity and metastability.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-021-00263-w