SOLVING SYSTEMS OF MONOTONE INCLUSIONS VIA PRIMAL-DUAL SPLITTING TECHNIQUES

• Published in: Taiwanese journal of mathematics Vol. 17; no. 6; pp. 1983 - 2009
• Main Authors: Boţ, Radu Ioan, Csetnek, Ernö Robert, Nagy, Erika
• Format: Journal Article
• Language: English
• Published: Mathematical Society of the Republic of China 01.12.2013
• Subjects: Hilbert spaces; Mathematical functions; Mathematical monotonicity; Mathematical vectors
• ISSN: 1027-5487; 2224-6851; 2224-6851
• DOI: 10.11650/tjm.17.2013.3087

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.