Radu Ioan Bot, Ernö Robert Csetnek, Erika Nagy: Solving systems of monotone inclusions via primal-dual splitting techniques

Author(s):

Radu Ioan Bot
Ernö Robert Csetnek
Erika Nagy

Title:

Radu Ioan Bot, Ernö Robert Csetnek, Erika Nagy: Solving systems of monotone inclusions via primal-dual splitting techniques

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 06, 2013

Mathematics Subject Classification:

47H05	[]
65K05	[]
90C25	[]
90C46	[]

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.

Keywords:

convex minimization, coupled systems, forward-backward-forward algorithm, monotone inclusion, operator splitting

Language:

English

Publication time:

03/2013