SOLVING SYSTEMS OF MONOTONE INCLUSIONS VIA PRIMAL-DUAL SPLITTING TECHNIQUES

In this paper we propose an algorithm for solving systems of coupled monotone inclusions in Hilbert spaces. The operators arising in each of the inclusions of the system are processed in each iteration separately, namely, the single-valued are evaluated explicitly (forward steps), while the set-valu...

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Published inTaiwanese journal of mathematics Vol. 17; no. 6; pp. 1983 - 2009
Main Authors Boţ, Radu Ioan, Csetnek, Ernö Robert, Nagy, Erika
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.12.2013
Subjects
Hilbert spaces
Mathematical functions
Mathematical monotonicity
Mathematical vectors
Online AccessGet full text
ISSN1027-5487
2224-6851
2224-6851
DOI10.11650/tjm.17.2013.3087

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Abstract In this paper we propose an algorithm for solving systems of coupled monotone inclusions in Hilbert spaces. The operators arising in each of the inclusions of the system are processed in each iteration separately, namely, the single-valued are evaluated explicitly (forward steps), while the set-valued ones via their resolvents (backward steps). In addition, most of the steps in the iterative scheme can be executed simultaneously, this making the method applicable to a variety of convex minimization problems. The numerical performances of the proposed splitting algorithm are emphasized through applications in average consensus on colored networks and image classification via support vector machines. 2010Mathematics Subject Classification: 47H05, 65K05, 90C25, 90C46. Key words and phrases: Convex minimization, Coupled systems, Forward-backward-forward algorithm, Monotone inclusion, Operator splitting.
AbstractList In this paper we propose an algorithm for solving systems of coupled monotone inclusions in Hilbert spaces. The operators arising in each of the inclusions of the system are processed in each iteration separately, namely, the single-valued are evaluated explicitly (forward steps), while the set-valued ones via their resolvents (backward steps). In addition, most of the steps in the iterative scheme can be executed simultaneously, this making the method applicable to a variety of convex minimization problems. The numerical performances of the proposed splitting algorithm are emphasized through applications in average consensus on colored networks and image classification via support vector machines. 2010Mathematics Subject Classification: 47H05, 65K05, 90C25, 90C46. Key words and phrases: Convex minimization, Coupled systems, Forward-backward-forward algorithm, Monotone inclusion, Operator splitting.
Author Nagy, Erika
Boţ, Radu Ioan
Csetnek, Ernö Robert
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Snippet In this paper we propose an algorithm for solving systems of coupled monotone inclusions in Hilbert spaces. The operators arising in each of the inclusions of...
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StartPage 1983
SubjectTerms Hilbert spaces
Mathematical functions
Mathematical monotonicity
Mathematical vectors
Title SOLVING SYSTEMS OF MONOTONE INCLUSIONS VIA PRIMAL-DUAL SPLITTING TECHNIQUES
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