Tight linear convergence rate bounds for Douglas-Rachford splitting and ADMM
Giselsson, Pontus LU
(2016)
54th IEEE Conference on Decision and Control, CDC 2015
2016.
p.3305-3310
- Abstract
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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/9e273773-ace9-4bbf-a306-1d8949a559f2
- author
- Giselsson, Pontus
LU
- organization
- publishing date
- 2016-02-08
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- host publication
- Proceedings of the IEEE Conference on Decision and Control
- volume
- 2016
- article number
- 7402716
- pages
- 6 pages
- publisher
- IEEE - Institute of Electrical and Electronics Engineers Inc.
- conference name
- 54th IEEE Conference on Decision and Control, CDC 2015
- conference location
- Osaka, Japan
- conference dates
- 2015-12-15 - 2015-12-18
- external identifiers
-
- scopus:84962013862
- ISBN
- 9781479978861
- DOI
- 10.1109/CDC.2015.7402716
- language
- English
- LU publication?
- yes
- id
- 9e273773-ace9-4bbf-a306-1d8949a559f2
- date added to LUP
- 2016-06-23 12:38:30
- date last changed
- 2023-10-24 01:23:20
@inproceedings{9e273773-ace9-4bbf-a306-1d8949a559f2,
abstract = {{<p>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.</p>}},
author = {{Giselsson, Pontus}},
booktitle = {{Proceedings of the IEEE Conference on Decision and Control}},
isbn = {{9781479978861}},
language = {{eng}},
month = {{02}},
pages = {{3305--3310}},
publisher = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
title = {{Tight linear convergence rate bounds for Douglas-Rachford splitting and ADMM}},
url = {{http://dx.doi.org/10.1109/CDC.2015.7402716}},
doi = {{10.1109/CDC.2015.7402716}},
volume = {{2016}},
year = {{2016}},
}