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2013 SOLVING SYSTEMS OF MONOTONE INCLUSIONS VIA PRIMAL-DUAL SPLITTING TECHNIQUES
Radu Ioan Boţ, Ernö Robert Csetnek, Erika Nagy
Taiwanese J. Math. 17(6): 1983-2009 (2013). DOI: 10.11650/tjm.17.2013.3087

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.

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Radu Ioan Boţ. Ernö Robert Csetnek. Erika Nagy. "SOLVING SYSTEMS OF MONOTONE INCLUSIONS VIA PRIMAL-DUAL SPLITTING TECHNIQUES." Taiwanese J. Math. 17 (6) 1983 - 2009, 2013. https://doi.org/10.11650/tjm.17.2013.3087

Information

Published: 2013
First available in Project Euclid: 10 July 2017

zbMATH: 1301.47080
MathSciNet: MR3141870
Digital Object Identifier: 10.11650/tjm.17.2013.3087

Subjects:
Primary: 47H05 , 65K05 , 90C25 , 90C46

Keywords: convex minimization , Coupled systems , forward-backward-forward algorithm , monotone inclusion , operator splitting

Rights: Copyright © 2013 The Mathematical Society of the Republic of China

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Vol.17 • No. 6 • 2013
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