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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. In: IEEE 53rd Annual Conference on Decision and Control (CDC), 2014, 15-17 December, 2014, Los Angeles, CA pp. 4234-4239. ISBN 978-1-4799-7746-8. (2014)

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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. By proving the equivalence between the Douglas-Rachford splitting method and a scaled gradient method applied to the DRE, results from smooth unconstrained optimization are employed to analyze convergence properties of DRS, to tune the method and to derive an accelerated version of it.

Item Type: Conference or Workshop Item (Paper)
Identification Number: 10.1109/CDC.2014.7040049
Uncontrolled Keywords: computational complexity;convergence;convex programming;gradient methods;DRE;DRS;Douglas-Rachford envelope;Douglas-Rachford splitting method;accelerated variants;complexity estimates;continuously differentiable function;convergence properties;convex composite optimization problems;scaled gradient method;smooth unconstrained optimization;Acceleration;Complexity theory;Convergence;Convex functions;Gradient methods;Radio frequency
Subjects: Q Science > QA Mathematics
Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Research Area: Computer Science and Applications
Depositing User: Caterina Tangheroni
Date Deposited: 11 Dec 2015 11:32
Last Modified: 11 Dec 2015 11:32
URI: http://eprints.imtlucca.it/id/eprint/2971

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