Solving monotone inclusions via compositions of nonexpansive averaged operators

A unified fixed point theoretic framework is proposed to investigate the asymptotic behavior of algorithms for finding solutions to monotone inclusion problems. The basic iterative scheme under consideration involves nonstationary compositions of perturbed averaged nonexpansive operators. The analys...

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Bibliographic Details
Published in:Optimization Vol. 53; no. 5-6; pp. 475 - 504
Main Author: Combettes, Patrick L.
Format: Journal Article
Language:English
Published: Philadelphia Taylor & Francis Group 01.10.2004
Taylor & Francis LLC
Subjects:
Algorithms
Averaged operator
Douglas-Rachford method
Forward-backward method
Mathematical models
Mathematics Subject Classifications 2000: 47B33
Monotone inclusion
Monotone operator
Optimization
Proximal point algorithm
Studies
ISSN:0233-1934, 1029-4945
Online Access:Get full text
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Summary:A unified fixed point theoretic framework is proposed to investigate the asymptotic behavior of algorithms for finding solutions to monotone inclusion problems. The basic iterative scheme under consideration involves nonstationary compositions of perturbed averaged nonexpansive operators. The analysis covers proximal methods for common zero problems as well as for various splitting methods for finding a zero of the sum of monotone operators.
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ISSN:0233-1934
1029-4945
DOI:10.1080/02331930412331327157