A strongly convergent Mann-type inertial algorithm for solving split variational inclusion problems

In this paper, we propose a new iterative method for finding an element of the solution set of a split variational inclusion problem in real Hilbert spaces. The iterative scheme is based on a well-known Mann-type method to obtain strong convergence and an inertial method to speed up the convergence...

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Published inOptimization and engineering Vol. 22; no. 1; pp. 159 - 185
Main Authors Anh, Pham Ky, Thong, Duong Viet, Dung, Vu Tien
Format Journal Article
LanguageEnglish
Published New York Springer US 01.03.2021
Springer Nature B.V
Subjects
Algorithms
Control
Convergence
Engineering
Environmental Management
Financial Engineering
Hilbert space
Iterative methods
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Research Article
Systems Theory
65K15
47H10
68W10
47H09
Split feasibility problem
Split variational inclusion problem
Mann-type method
65Y05
47H06
Online AccessGet full text
ISSN1389-4420
1573-2924
DOI10.1007/s11081-020-09501-2

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Summary:In this paper, we propose a new iterative method for finding an element of the solution set of a split variational inclusion problem in real Hilbert spaces. The iterative scheme is based on a well-known Mann-type method to obtain strong convergence and an inertial method to speed up the convergence rate. We also apply the proposed algorithm to studying the split feasibility problem. Finally, we give some numerical results which show that our proposed algorithm is efficient and implementable from the numerical point of view.
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ISSN:1389-4420
1573-2924
DOI:10.1007/s11081-020-09501-2