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A Douglas-Rachford type primal-dual method for solving inclusions with mixtures of composite and parallel-sum type monotone operators

Radu Ioan Bot(radu.bot***at***mathematik.tu-chemnitz.de)
Christopher Hendrich(christopher.hendrich***at***mathematik.tu-chemnitz.de)

Abstract: In this paper we propose two different primal-dual splitting algorithms for solving inclusions involving mixtures of composite and parallel-sum type monotone operators which rely on an inexact Douglas-Rachford splitting method, however applied in different underlying Hilbert spaces. Most importantly, the algorithms allow to process the bounded linear operators and the set-valued operators occurring in the formulation of the monotone inclusion problem separately at each iteration, the latter being individually accessed via their resolvents. The performances of the primal-dual algorithms are emphasized via some numerical experiments on location and image deblurring problems.

Keywords: Douglas-Rachford splitting, monotone inclusion, Fenchel duality, convex optimization

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Citation:

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Entry Submitted: 12/03/2012
Entry Accepted: 12/03/2012
Entry Last Modified: 12/03/2012

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