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Fixing and extending some recent results on the ADMM algorithm

Banert, Sebastian LU ; Boţ, Radu Ioan and Csetnek, Ernö Robert (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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author
; and
organization
publishing date
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
2024-06-12 16:10:12
@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}},
}