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Douglas-Rachford splitting: complexity estimates and accelerated variants

Patrinos, Panagiotis and Stella, Lorenzo and Bemporad, Alberto Douglas-Rachford splitting: complexity estimates and accelerated variants. Working Paper # /2014 ArXiv (Unpublished)

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We propose a new approach for analyzing convergence of the Douglas-Rachford splitting method for solving convex composite optimization problems. The approach is based on a continuously differentiable function, the Douglas-Rachford Envelope (DRE), whose stationary points correspond to the solutions of the original (possibly nonsmooth) problem. The Douglas-Rachford splitting method is shown to be equivalent to a scaled gradient method on the DRE, and so results from smooth unconstrained optimization are employed to analyze its convergence and optimally choose parameter {\gamma} and to derive an accelerated variant of Douglas-Rachford splitting.

Item Type: Working Paper (Working Paper)
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
T Technology > T Technology (General)
Research Area: Computer Science and Applications
Depositing User: Ms T. Iannizzi
Date Deposited: 02 Sep 2014 09:44
Last Modified: 02 Sep 2014 09:44
URI: http://eprints.imtlucca.it/id/eprint/2273

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