Inertial Douglas–Rachford splitting for monotone inclusion problems

We propose an inertial Douglas–Rachford splitting algorithm for finding the set of zeros of the sum of two maximally monotone operators in Hilbert spaces and investigate its convergence properties. To this end we formulate first the inertial version of the Krasnosel’skiı̆–Mann algorithm for approxim...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 256; pp. 472 - 487
Main Authors: Boţ, Radu Ioan, Csetnek, Ernö Robert, Hendrich, Christopher
Format: Journal Article
Language:English
Published: Elsevier Inc 01.04.2015
Subjects:
Convex optimization
Douglas–Rachford splitting
Inertial splitting algorithm
Krasnosel’skiı̆–Mann algorithm
Primal–dual algorithm
Douglas–Rachford splitting
Krasnosel’skiı̆–Mann algorithm
Convex optimization
Primal–dual algorithm
Inertial splitting algorithm
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Summary:We propose an inertial Douglas–Rachford splitting algorithm for finding the set of zeros of the sum of two maximally monotone operators in Hilbert spaces and investigate its convergence properties. To this end we formulate first the inertial version of the Krasnosel’skiı̆–Mann algorithm for approximating the set of fixed points of a nonexpansive operator, for which we also provide an exhaustive convergence analysis. By using a product space approach we employ these results to the solving of monotone inclusion problems involving linearly composed and parallel-sum type operators and provide in this way iterative schemes where each of the maximally monotone mappings is accessed separately via its resolvent. We consider also the special instance of solving a primal–dual pair of nonsmooth convex optimization problems and illustrate the theoretical results via some numerical experiments in clustering and location theory.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2015.01.017