A Strongly Convergent Viscosity-Type Inertial Algorithm with Self Adaptive Stepsize for Solving Split Variational Inclusion Problems in Hilbert Spaces

In this paper, we propose a new algorithm with inertial term and self-adaptive stepsize for solving the split variational inclusion problem (denoted by SVIP) in real Hilbert spaces. Under suitable conditions imposed on the parameters, we prove that our iterative scheme converges strongly to an eleme...

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Bibliographic Details
Published inNetworks and spatial economics Vol. 23; no. 4; pp. 931 - 952
Main Authors Xia, Pingjing, Cai, Gang, Dong, Qiao-Li
Format Journal Article
LanguageEnglish
Published New York Springer US 01.12.2023
Springer Nature B.V
Subjects
Adaptive algorithms
Algorithms
Civil Engineering
Convergence
Economic activity
Economics
Economics and Finance
Hilbert space
Iterative methods
Operations Research/Decision Theory
Regional/Spatial Science
Viscosity
Strong convergence
47H10
Viscosity-type method
Inertial method
47H07
Split variational inclusion problem
47H05
Self adaptive stepsize
54H25
Online AccessGet full text
ISSN1566-113X
1572-9427
DOI10.1007/s11067-023-09600-4

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Summary:In this paper, we propose a new algorithm with inertial term and self-adaptive stepsize for solving the split variational inclusion problem (denoted by SVIP) in real Hilbert spaces. Under suitable conditions imposed on the parameters, we prove that our iterative scheme converges strongly to an element of the solution set of SVIP without the prior knowledge of the operator norm. Furthermore, we demonstrate that our suggested algorithm is efficient and achievable through some numerical experiments.
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ISSN:1566-113X
1572-9427
DOI:10.1007/s11067-023-09600-4