Strong Convergence of the Modified Inertial Extragradient Method with Line-Search Process for Solving Variational Inequality Problems in Hilbert Spaces

2021 ◽  
Vol 88 (3) ◽  
Author(s):  
Zhongbing Xie ◽  
Gang Cai ◽  
Xiaoxiao Li ◽  
Qiao-Li Dong
Keyword(s):  
Variational Inequality ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Line Search ◽  
Extragradient Method ◽  
Variational Inequality Problems ◽  
Search Process

A new self adaptive Tseng’s extragradient method with double-projection for solving pseudomonotone variational inequality problems in Hilbert spaces

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Zhongbing Xie ◽  
Gang Cai ◽  
Xiaoxiao Li ◽  
Qiao-Li Dong
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Convergence Theorem ◽  
Numerical Experiments ◽  
Extragradient Method ◽  
Variational Inequality Problems ◽  
Strong Convergence Theorem ◽  
Tseng’S Extragradient Method

Abstract The purpose of this paper is to study a new Tseng’s extragradient method with two different stepsize rules for solving pseudomonotone variational inequalities in real Hilbert spaces. We prove a strong convergence theorem of the proposed algorithm under some suitable conditions imposed on the parameters. Moreover, we also give some numerical experiments to demonstrate the performance of our algorithm.

scholarly journals PARALLEL EXTRAGRADIENT-PROXIMAL METHODS FOR SPLIT EQUILIBRIUM PROBLEMS

2016 ◽  
Vol 21 (4) ◽  
pp. 478-501 ◽  
Author(s):  
Dang Van Hieu
Keyword(s):  
Variational Inequality ◽  
Strong Convergence ◽  
Projection Method ◽  
Equilibrium Problems ◽  
Extragradient Method ◽  
Variational Inequality Problems ◽  
Proximal Methods ◽  
Proximal Method ◽  
Weak And Strong Convergence ◽  
Split Variational Inequality

In this paper, we introduce two parallel extragradient-proximal methods for solving split equilibrium problems. The algorithms combine the extragradient method, the proximal method and the shrinking projection method. The weak and strong convergence theorems for iterative sequences generated by the algorithms are established under widely used assumptions for equilibrium bifunctions. We also present an application to split variational inequality problems and a numerical example to illustrate the convergence of the proposed algorithms.

scholarly journals Two modifications of the inertial Tseng extragradient method with self-adaptive step size for solving monotone variational inequality problems

2020 ◽  
Vol 53 (1) ◽  
pp. 208-224 ◽  
Author(s):  
Timilehin Opeyemi Alakoya ◽  
Lateef Olakunle Jolaoso ◽  
Oluwatosin Temitope Mewomo
Keyword(s):  
Variational Inequality ◽  
Strong Convergence ◽  
Extragradient Method ◽  
Lipschitz Constant ◽  
Monotone Mapping ◽  
Variational Inequality Problems ◽  
Step Size ◽  
Lipschitz Continuous ◽  
Convergence Results ◽  
Monotone Variational Inequality

AbstractIn this work, we introduce two new inertial-type algorithms for solving variational inequality problems (VIPs) with monotone and Lipschitz continuous mappings in real Hilbert spaces. The first algorithm requires the computation of only one projection onto the feasible set per iteration while the second algorithm needs the computation of only one projection onto a half-space, and prior knowledge of the Lipschitz constant of the monotone mapping is not required in proving the strong convergence theorems for the two algorithms. Under some mild assumptions, we prove strong convergence results for the proposed algorithms to a solution of a VIP. Finally, we provide some numerical experiments to illustrate the efficiency and advantages of the proposed algorithms.

scholarly journals Multi-Step Inertial Regularized Methods for Hierarchical Variational Inequality Problems Involving Generalized Lipschitzian Mappings

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2103
Author(s):  
Bingnan Jiang ◽  
Yuanheng Wang ◽  
Jen-Chih Yao
Keyword(s):  
Variational Inequality ◽  
Strong Convergence ◽  
Iterative Methods ◽  
Hilbert Spaces ◽  
Numerical Experiments ◽  
Variational Inequality Problems ◽  
Convergence Theorems ◽  
Lipschitzian Mappings ◽  
Regularized Methods

In this paper, we construct two multi-step inertial regularized methods for hierarchical inequality problems involving generalized Lipschitzian and hemicontinuous mappings in Hilbert spaces. Then we present two strong convergence theorems and some numerical experiments to show the effectiveness and feasibility of our new iterative methods.

scholarly journals A Generalized Strong Convergence Algorithm in the Presence of Errors for Variational Inequality Problems in Hilbert Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Mostafa Ghadampour ◽  
Donal O’Regan ◽  
Ebrahim Soori ◽  
Ravi P. Agarwal
Keyword(s):  
Variational Inequality ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Variational Inequality Problem ◽  
Numerical Algorithms ◽  
Variational Inequality Problems ◽  
Numerical Examples ◽  
Inequality Problem ◽  
Convergence Of An Algorithm ◽  
Computational Errors

In this paper, we study the strong convergence of an algorithm to solve the variational inequality problem which extends a recent paper (Thong et al., Numerical Algorithms. 78, 1045-1060 (2018)). We reduce and refine some of their algorithm conditions and we prove the convergence of the algorithm in the presence of some computational errors. Then, using the MATLAB software, the result will be illustrated with some numerical examples. Also, we compare our algorithm with some other well-known algorithms.

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