A Douglas--Rachford Type Primal-Dual Method for Solving Inclusions with Mixtures of Composite and Parallel-Sum Type Monotone Operators

Authors:
  • RBRadu Ioan Boţ
    Radu Ioan Boţ
  • CHChristopher Hendrich
    Christopher Hendrich
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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, but applied in different underlying Hilbert spaces. Most importantly, the algorithms allow one 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 performance of the primal-dual algorithms is emphasized via some numerical experiments on location and image denoising problems.

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