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An improved inertial extragradient subgradient method for solving split variational inequality problems

An improved inertial extragradient subgradient method for solving split variational inequality... The main purpose of this paper is to study the split variational inequality problem in real Hilbert spaces. For solving this problem, we propose a new inertial method which combines advantages of the subgradient extragradient method and the projection contraction method. Similar to some recent developments for solving this problem the cost operators are pseudomonotone and uniformly continuous and do not require the knowledge of the Lipschitz constant associated with the variational inequality mapping. We prove that the proposed method converges strongly to a minimum norm solution of the problem and numerical examples are given to support our theoretical findings. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Boletín de la Sociedad Matemática Mexicana Springer Journals

An improved inertial extragradient subgradient method for solving split variational inequality problems

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References (65)

Publisher
Springer Journals
Copyright
Copyright © Sociedad Matemática Mexicana 2022
ISSN
1405-213X
eISSN
2296-4495
DOI
10.1007/s40590-021-00408-1
Publisher site
See Article on Publisher Site

Abstract

The main purpose of this paper is to study the split variational inequality problem in real Hilbert spaces. For solving this problem, we propose a new inertial method which combines advantages of the subgradient extragradient method and the projection contraction method. Similar to some recent developments for solving this problem the cost operators are pseudomonotone and uniformly continuous and do not require the knowledge of the Lipschitz constant associated with the variational inequality mapping. We prove that the proposed method converges strongly to a minimum norm solution of the problem and numerical examples are given to support our theoretical findings.

Journal

Boletín de la Sociedad Matemática MexicanaSpringer Journals

Published: Mar 1, 2022

Keywords: Projection and contraction method; Subgradient extragradient method; Split feasibility problem; Pseudomonotone mapping; Inertial technique; 47H09; 47H10; 49J20; 49J40

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