Inertial Douglas–Rachford splitting for monotone inclusion problems

Radu Ioan Boţ, Ernö Robert Csetnek and Christopher Hendrich

Applied Mathematics and Computation, 2015, vol. 256, issue C, 472-487

Abstract: 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.

Keywords: Inertial splitting algorithm; Douglas–Rachford splitting; Krasnosel’skiı̆–Mann algorithm; Primal–dual algorithm; Convex optimization (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (31)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:256:y:2015:i:c:p:472-487

DOI: 10.1016/j.amc.2015.01.017

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