New generalized variable stepsizes of the CQ algorithm for solving the split feasibility problem

Variable stepsize methods are effective for various modified CQ algorithms to solve the split feasibility problem (SFP). The purpose of this paper is first to introduce two new simpler variable stepsizes of the CQ algorithm. Then two new generalized variable stepsizes which can cover the former ones...

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Detalles Bibliográficos
Autores principales: Wang, Peiyuan, Zhou, Jianjun, Wang, Risheng, Chen, Jie
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2017
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5488062/
https://www.ncbi.nlm.nih.gov/pubmed/28680238
http://dx.doi.org/10.1186/s13660-017-1409-9
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author Wang, Peiyuan
Zhou, Jianjun
Wang, Risheng
Chen, Jie
author_facet Wang, Peiyuan
Zhou, Jianjun
Wang, Risheng
Chen, Jie
author_sort Wang, Peiyuan
collection PubMed
description Variable stepsize methods are effective for various modified CQ algorithms to solve the split feasibility problem (SFP). The purpose of this paper is first to introduce two new simpler variable stepsizes of the CQ algorithm. Then two new generalized variable stepsizes which can cover the former ones are also proposed in real Hilbert spaces. And then, two more general KM (Krasnosel’skii-Mann)-CQ algorithms are also presented. Several weak and strong convergence properties are established. Moreover, some numerical experiments have been taken to illustrate the performance of the proposed stepsizes and algorithms.
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spelling pubmed-54880622017-07-03 New generalized variable stepsizes of the CQ algorithm for solving the split feasibility problem Wang, Peiyuan Zhou, Jianjun Wang, Risheng Chen, Jie J Inequal Appl Research Variable stepsize methods are effective for various modified CQ algorithms to solve the split feasibility problem (SFP). The purpose of this paper is first to introduce two new simpler variable stepsizes of the CQ algorithm. Then two new generalized variable stepsizes which can cover the former ones are also proposed in real Hilbert spaces. And then, two more general KM (Krasnosel’skii-Mann)-CQ algorithms are also presented. Several weak and strong convergence properties are established. Moreover, some numerical experiments have been taken to illustrate the performance of the proposed stepsizes and algorithms. Springer International Publishing 2017-06-12 2017 /pmc/articles/PMC5488062/ /pubmed/28680238 http://dx.doi.org/10.1186/s13660-017-1409-9 Text en © The Author(s) 2017 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
Wang, Peiyuan
Zhou, Jianjun
Wang, Risheng
Chen, Jie
New generalized variable stepsizes of the CQ algorithm for solving the split feasibility problem
title New generalized variable stepsizes of the CQ algorithm for solving the split feasibility problem
title_full New generalized variable stepsizes of the CQ algorithm for solving the split feasibility problem
title_fullStr New generalized variable stepsizes of the CQ algorithm for solving the split feasibility problem
title_full_unstemmed New generalized variable stepsizes of the CQ algorithm for solving the split feasibility problem
title_short New generalized variable stepsizes of the CQ algorithm for solving the split feasibility problem
title_sort new generalized variable stepsizes of the cq algorithm for solving the split feasibility problem
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5488062/
https://www.ncbi.nlm.nih.gov/pubmed/28680238
http://dx.doi.org/10.1186/s13660-017-1409-9
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