Fixing and extending some recent results on the ADMM algorithm

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 a...

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Autores principales: Banert, Sebastian, Boţ, Radu Ioan, Csetnek, Ernö Robert
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer US 2020
Materias:
Original Paper
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7862544/
https://www.ncbi.nlm.nih.gov/pubmed/33603318
http://dx.doi.org/10.1007/s11075-020-00934-5
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author Banert, Sebastian
Boţ, Radu Ioan
Csetnek, Ernö Robert
author_facet Banert, Sebastian
Boţ, Radu Ioan
Csetnek, Ernö Robert
author_sort Banert, Sebastian
collection PubMed
description 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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spelling pubmed-78625442021-02-16 Fixing and extending some recent results on the ADMM algorithm Banert, Sebastian Boţ, Radu Ioan Csetnek, Ernö Robert Numer Algorithms Original Paper 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. Springer US 2020-05-14 2021 /pmc/articles/PMC7862544/ /pubmed/33603318 http://dx.doi.org/10.1007/s11075-020-00934-5 Text en © The Author(s) 2020 Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
spellingShingle Original Paper
Banert, Sebastian
Boţ, Radu Ioan
Csetnek, Ernö Robert
Fixing and extending some recent results on the ADMM algorithm
title Fixing and extending some recent results on the ADMM algorithm
title_full Fixing and extending some recent results on the ADMM algorithm
title_fullStr Fixing and extending some recent results on the ADMM algorithm
title_full_unstemmed Fixing and extending some recent results on the ADMM algorithm
title_short Fixing and extending some recent results on the ADMM algorithm
title_sort fixing and extending some recent results on the admm algorithm
topic Original Paper
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7862544/
https://www.ncbi.nlm.nih.gov/pubmed/33603318
http://dx.doi.org/10.1007/s11075-020-00934-5
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