On compositions of special cases of Lipschitz continuous operators
(2021) In Fixed Point Theory and Algorithms for Sciences and Engineering 2021(1).- Abstract
Many iterative optimization algorithms involve compositions of special cases of Lipschitz continuous operators, namely firmly nonexpansive, averaged, and nonexpansive operators. The structure and properties of the compositions are of particular importance in the proofs of convergence of such algorithms. In this paper, we systematically study the compositions of further special cases of Lipschitz continuous operators. Applications of our results include compositions of scaled conically nonexpansive mappings, as well as the Douglas–Rachford and forward–backward operators, when applied to solve certain structured monotone inclusion and optimization problems. Several examples illustrate and tighten our conclusions.
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- author
- Giselsson, Pontus LU and Moursi, Walaa M.
- organization
- publishing date
- 2021-12
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Compositions of operators, Conically nonexpansive operators, Douglas–Rachford algorithm, Forward-backward algorithm, Hypoconvex function, Maximally monotone operator, Proximal operator, Resolvent
- in
- Fixed Point Theory and Algorithms for Sciences and Engineering
- volume
- 2021
- issue
- 1
- article number
- 25
- publisher
- Springer
- external identifiers
-
- pmid:34993526
- scopus:85121491628
- ISSN
- 1687-1820
- DOI
- 10.1186/s13663-021-00709-0
- language
- English
- LU publication?
- yes
- additional info
- Publisher Copyright: © 2021, The Author(s).
- id
- 2d3256b0-afb8-450e-a575-030219e524f5
- date added to LUP
- 2022-02-21 09:19:02
- date last changed
- 2024-09-15 18:08:08
@article{2d3256b0-afb8-450e-a575-030219e524f5, abstract = {{<p>Many iterative optimization algorithms involve compositions of special cases of Lipschitz continuous operators, namely firmly nonexpansive, averaged, and nonexpansive operators. The structure and properties of the compositions are of particular importance in the proofs of convergence of such algorithms. In this paper, we systematically study the compositions of further special cases of Lipschitz continuous operators. Applications of our results include compositions of scaled conically nonexpansive mappings, as well as the Douglas–Rachford and forward–backward operators, when applied to solve certain structured monotone inclusion and optimization problems. Several examples illustrate and tighten our conclusions.</p>}}, author = {{Giselsson, Pontus and Moursi, Walaa M.}}, issn = {{1687-1820}}, keywords = {{Compositions of operators; Conically nonexpansive operators; Douglas–Rachford algorithm; Forward-backward algorithm; Hypoconvex function; Maximally monotone operator; Proximal operator; Resolvent}}, language = {{eng}}, number = {{1}}, publisher = {{Springer}}, series = {{Fixed Point Theory and Algorithms for Sciences and Engineering}}, title = {{On compositions of special cases of Lipschitz continuous operators}}, url = {{http://dx.doi.org/10.1186/s13663-021-00709-0}}, doi = {{10.1186/s13663-021-00709-0}}, volume = {{2021}}, year = {{2021}}, }