Linear Convergence and Metric Selection for Douglas-Rachford Splitting and ADMM
(2017) In IEEE Transactions on Automatic Control 62(2). p.532-544- Abstract
Recently, several convergence rate results for Douglas-Rachford splitting and the alternating direction method of multipliers (ADMM) have been presented in the literature. In this paper, we show global linear convergence rate bounds for Douglas-Rachford splitting and ADMM under strong convexity and smoothness assumptions. We further show that the rate bounds are tight for the class of problems under consideration for all feasible algorithm parameters. For problems that satisfy the assumptions, we show how to select step-size and metric for the algorithm that optimize the derived convergence rate bounds. For problems with a similar structure that do not satisfy the assumptions, we present heuristic step-size and metric selection... (More)
Recently, several convergence rate results for Douglas-Rachford splitting and the alternating direction method of multipliers (ADMM) have been presented in the literature. In this paper, we show global linear convergence rate bounds for Douglas-Rachford splitting and ADMM under strong convexity and smoothness assumptions. We further show that the rate bounds are tight for the class of problems under consideration for all feasible algorithm parameters. For problems that satisfy the assumptions, we show how to select step-size and metric for the algorithm that optimize the derived convergence rate bounds. For problems with a similar structure that do not satisfy the assumptions, we present heuristic step-size and metric selection methods.
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- author
- Giselsson, Pontus LU and Boyd, Stephen
- organization
- publishing date
- 2017-02-01
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Alternating direction method of multipliers (ADMM), Douglas-Rachford splitting, linear convergence, optimization algorithms
- in
- IEEE Transactions on Automatic Control
- volume
- 62
- issue
- 2
- article number
- 7465685
- pages
- 13 pages
- publisher
- IEEE - Institute of Electrical and Electronics Engineers Inc.
- external identifiers
-
- wos:000395510600002
- scopus:85011591304
- ISSN
- 0018-9286
- DOI
- 10.1109/TAC.2016.2564160
- language
- English
- LU publication?
- yes
- id
- 8c6c0231-0b4e-4166-acd5-98d81f36ec74
- date added to LUP
- 2017-02-15 12:47:36
- date last changed
- 2024-09-15 19:24:01
@article{8c6c0231-0b4e-4166-acd5-98d81f36ec74, abstract = {{<p>Recently, several convergence rate results for Douglas-Rachford splitting and the alternating direction method of multipliers (ADMM) have been presented in the literature. In this paper, we show global linear convergence rate bounds for Douglas-Rachford splitting and ADMM under strong convexity and smoothness assumptions. We further show that the rate bounds are tight for the class of problems under consideration for all feasible algorithm parameters. For problems that satisfy the assumptions, we show how to select step-size and metric for the algorithm that optimize the derived convergence rate bounds. For problems with a similar structure that do not satisfy the assumptions, we present heuristic step-size and metric selection methods.</p>}}, author = {{Giselsson, Pontus and Boyd, Stephen}}, issn = {{0018-9286}}, keywords = {{Alternating direction method of multipliers (ADMM); Douglas-Rachford splitting; linear convergence; optimization algorithms}}, language = {{eng}}, month = {{02}}, number = {{2}}, pages = {{532--544}}, publisher = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}}, series = {{IEEE Transactions on Automatic Control}}, title = {{Linear Convergence and Metric Selection for Douglas-Rachford Splitting and ADMM}}, url = {{http://dx.doi.org/10.1109/TAC.2016.2564160}}, doi = {{10.1109/TAC.2016.2564160}}, volume = {{62}}, year = {{2017}}, }