Strong convergence and bounded perturbation resilience of a modified proximal gradient algorithm

The proximal gradient algorithm is an appealing approach in finding solutions of non-smooth composite optimization problems, which may only has weak convergence in the infinite-dimensional setting. In this paper, we introduce a modified proximal gradient algorithm with outer perturbations in Hilbert...

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Detalles Bibliográficos
Autores principales: Guo, Yanni, Cui, Wei
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5932141/
https://www.ncbi.nlm.nih.gov/pubmed/29755243
http://dx.doi.org/10.1186/s13660-018-1695-x
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author Guo, Yanni
Cui, Wei
author_facet Guo, Yanni
Cui, Wei
author_sort Guo, Yanni
collection PubMed
description The proximal gradient algorithm is an appealing approach in finding solutions of non-smooth composite optimization problems, which may only has weak convergence in the infinite-dimensional setting. In this paper, we introduce a modified proximal gradient algorithm with outer perturbations in Hilbert space and prove that the algorithm converges strongly to a solution of the composite optimization problem. We also discuss the bounded perturbation resilience of the basic algorithm of this iterative scheme and illustrate it with an application.
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spelling pubmed-59321412018-05-09 Strong convergence and bounded perturbation resilience of a modified proximal gradient algorithm Guo, Yanni Cui, Wei J Inequal Appl Research The proximal gradient algorithm is an appealing approach in finding solutions of non-smooth composite optimization problems, which may only has weak convergence in the infinite-dimensional setting. In this paper, we introduce a modified proximal gradient algorithm with outer perturbations in Hilbert space and prove that the algorithm converges strongly to a solution of the composite optimization problem. We also discuss the bounded perturbation resilience of the basic algorithm of this iterative scheme and illustrate it with an application. Springer International Publishing 2018-05-02 2018 /pmc/articles/PMC5932141/ /pubmed/29755243 http://dx.doi.org/10.1186/s13660-018-1695-x Text en © The Author(s) 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Guo, Yanni
Cui, Wei
Strong convergence and bounded perturbation resilience of a modified proximal gradient algorithm
title Strong convergence and bounded perturbation resilience of a modified proximal gradient algorithm
title_full Strong convergence and bounded perturbation resilience of a modified proximal gradient algorithm
title_fullStr Strong convergence and bounded perturbation resilience of a modified proximal gradient algorithm
title_full_unstemmed Strong convergence and bounded perturbation resilience of a modified proximal gradient algorithm
title_short Strong convergence and bounded perturbation resilience of a modified proximal gradient algorithm
title_sort strong convergence and bounded perturbation resilience of a modified proximal gradient algorithm
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5932141/
https://www.ncbi.nlm.nih.gov/pubmed/29755243
http://dx.doi.org/10.1186/s13660-018-1695-x
work_keys_str_mv AT guoyanni strongconvergenceandboundedperturbationresilienceofamodifiedproximalgradientalgorithm
AT cuiwei strongconvergenceandboundedperturbationresilienceofamodifiedproximalgradientalgorithm

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