Fixing and extending some recent results on the ADMM algorithm
(2021) In Numerical Algorithms 86(3). p.1303-1325- Abstract
We investigate the techniques and ideas used in Shefi and Teboulle (SIAM J Optim 24(1), 269–297, 2014) in the convergence analysis of two proximal ADMM algorithms for solving convex optimization problems involving compositions with linear operators. Besides this, we formulate a variant of the ADMM algorithm that is able to handle convex optimization problems involving an additional smooth function in its objective, and which is evaluated through its gradient. Moreover, in each iteration, we allow the use of variable metrics, while the investigations are carried out in the setting of infinite-dimensional Hilbert spaces. This algorithmic scheme is investigated from the point of view of its convergence properties.
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https://lup.lub.lu.se/record/c1cf181c-e276-463c-b565-8b074fecc87d
- author
- Banert, Sebastian LU ; Boţ, Radu Ioan and Csetnek, Ernö Robert
- organization
- publishing date
- 2021
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- ADMM algorithm, Lagrangian, Positive semidefinite operators, Saddle points, Variable metrics
- in
- Numerical Algorithms
- volume
- 86
- issue
- 3
- pages
- 1303 - 1325
- publisher
- Springer
- external identifiers
-
- scopus:85085013011
- pmid:33603318
- ISSN
- 1017-1398
- DOI
- 10.1007/s11075-020-00934-5
- language
- English
- LU publication?
- yes
- id
- c1cf181c-e276-463c-b565-8b074fecc87d
- date added to LUP
- 2020-06-26 13:51:54
- date last changed
- 2024-06-26 17:44:53
@article{c1cf181c-e276-463c-b565-8b074fecc87d, abstract = {{<p>We investigate the techniques and ideas used in Shefi and Teboulle (SIAM J Optim 24(1), 269–297, 2014) in the convergence analysis of two proximal ADMM algorithms for solving convex optimization problems involving compositions with linear operators. Besides this, we formulate a variant of the ADMM algorithm that is able to handle convex optimization problems involving an additional smooth function in its objective, and which is evaluated through its gradient. Moreover, in each iteration, we allow the use of variable metrics, while the investigations are carried out in the setting of infinite-dimensional Hilbert spaces. This algorithmic scheme is investigated from the point of view of its convergence properties.</p>}}, author = {{Banert, Sebastian and Boţ, Radu Ioan and Csetnek, Ernö Robert}}, issn = {{1017-1398}}, keywords = {{ADMM algorithm; Lagrangian; Positive semidefinite operators; Saddle points; Variable metrics}}, language = {{eng}}, number = {{3}}, pages = {{1303--1325}}, publisher = {{Springer}}, series = {{Numerical Algorithms}}, title = {{Fixing and extending some recent results on the ADMM algorithm}}, url = {{http://dx.doi.org/10.1007/s11075-020-00934-5}}, doi = {{10.1007/s11075-020-00934-5}}, volume = {{86}}, year = {{2021}}, }