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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Vydané v:	Optimization Ročník 53; číslo 5-6; s. 475 - 504
Hlavný autor:	Combettes, Patrick L.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Philadelphia Taylor & Francis Group 01.10.2004 Taylor & Francis LLC
Predmet:	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
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Abstract	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.
AbstractList	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. [PUBLICATION ABSTRACT] 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.
Author	Combettes, Patrick L.
Author_xml	– sequence: 1 givenname: Patrick L. surname: Combettes fullname: Combettes, Patrick L.
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Snippet	A unified fixed point theoretic framework is proposed to investigate the asymptotic behavior of algorithms for finding solutions to monotone inclusion...
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SubjectTerms	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
Title	Solving monotone inclusions via compositions of nonexpansive averaged operators
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