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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Vydáno v:Applied mathematics and computation Ročník 256; s. 472 - 487
Hlavní autoři: Boţ, Radu Ioan, Csetnek, Ernö Robert, Hendrich, Christopher
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Inc 01.04.2015
Témata:
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
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Shrnutí: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