Journal
SIAM JOURNAL ON OPTIMIZATION
Volume 23, Issue 4, Pages 2541-2565Publisher
SIAM PUBLICATIONS
DOI: 10.1137/120901106
Keywords
Douglas-Rachford splitting; monotone inclusion; Fenchel duality; convex optimization
Categories
Funding
- DFG (German Research Foundation) [BO 2516/4-1]
- Free State Saxony, Germany
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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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