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Tight linear convergence rate bounds for Douglas-Rachford splitting and ADMM

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Author

Summary, in English

Douglas-Rachford splitting and the alternating direction method of multipliers (ADMM) can be used to solve convex optimization problems that consist of a sum of two functions. Convergence rate estimates for these algorithms have received much attention lately. In particular, linear convergence rates have been shown by several authors under various assumptions. One such set of assumptions is strong convexity and smoothness of one of the functions in the minimization problem. The authors recently provided a linear convergence rate bound for such problems. In this paper, we show that this rate bound is tight for the class of problems under consideration.

Publishing year

2016-02-08

Language

English

Pages

3305-3310

Publication/Series

Proceedings of the IEEE Conference on Decision and Control

Volume

2016

Document type

Conference paper

Publisher

IEEE - Institute of Electrical and Electronics Engineers Inc.

Topic

  • Mathematics

Conference name

54th IEEE Conference on Decision and Control, CDC 2015

Conference date

2015-12-15 - 2015-12-18

Conference place

Osaka, Japan

Status

Published

ISBN/ISSN/Other

  • ISBN: 9781479978861