A method with inertial extrapolation step for split monotone inclusion problems

The purpose of this paper is to study the convergence analysis of an iterative algorithm with inertial extrapolation step for finding an approximate solution of split monotone inclusion problem in real Hilbert spaces. Weak convergence of the sequence of iterates generated from the proposed method is...

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Published inOptimization Vol. 70; no. 4; pp. 741 - 761
Main Authors Yao, Yonghong, Shehu, Yekini, Li, Xiao-Huan, Dong, Qiao-Li
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 03.04.2021
Taylor & Francis LLC
Subjects
Convergence
Extrapolation
Hilbert space
Hilbert spaces
inertial extrapolation step
Iterative algorithms
Iterative methods
numerical examples
Split monotone inclusion
weak convergence
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ISSN0233-1934
1029-4945
DOI10.1080/02331934.2020.1857754

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Summary:The purpose of this paper is to study the convergence analysis of an iterative algorithm with inertial extrapolation step for finding an approximate solution of split monotone inclusion problem in real Hilbert spaces. Weak convergence of the sequence of iterates generated from the proposed method is obtained under some mild assumptions. Some special cases of the general problem are given and we give some numerical implementations to support the theoretical analysis and give justification for the addition of the extrapolation step in the proposed method.
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ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2020.1857754