scholarly journals A Mean Extragradient Method for Solving Variational Inequalities

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 462
Author(s):  
Apichit Buakird ◽  
Nimit Nimana ◽  
Narin Petrot
Keyword(s):  
Hilbert Space ◽  
Variational Inequality ◽  
Weak Convergence ◽  
Numerical Experiments ◽  
Variational Inequality Problem ◽  
Extragradient Method ◽  
Mean Value ◽  
Inequality Problem ◽  
The Mean ◽  
Mean Value Method

We propose a modified extragradient method for solving the variational inequality problem in a Hilbert space. The method is a combination of the well-known subgradient extragradient with the Mann’s mean value method in which the updated iterate is picked in the convex hull of all previous iterates. We show weak convergence of the mean value iterate to a solution of the variational inequality problem, provided that a condition on the corresponding averaging matrix is fulfilled. Some numerical experiments are given to show the effectiveness of the obtained theoretical result.

INERTIAL RELAXED TSENG METHOD FOR SOLVING VARIATIONAL INEQUALITY PROBLEM IN HILBERT SPACE

2021 ◽  
Vol 10 (12) ◽  
pp. 3597-3623
Author(s):  
F. Akusah ◽  
A.A. Mebawondu ◽  
H.A. Abass ◽  
M.O. Aibinu ◽  
O.K. Narain
Keyword(s):  
Hilbert Space ◽  
Variational Inequality ◽  
Strong Convergence ◽  
Numerical Experiments ◽  
Variational Inequality Problem ◽  
Extrapolation Method ◽  
Minimum Norm ◽  
Minimum Norm Solution ◽  
Inequality Problem ◽  
Weaker Conditions

The research efforts of this paper is to present a new inertial relaxed Tseng extrapolation method with weaker conditions for approximating the solution of a variational inequality problem, where the underlying operator is only required to be pseudomonotone. The strongly pseudomonotonicity and inverse strongly monotonicity assumptions which the existing literature used are successfully weakened. The strong convergence of the proposed method to a minimum-norm solution of a variational inequality problem are established. Furthermore, we present an application and some numerical experiments to show the efficiency and applicability of our method in comparison with other methods in the literature.

scholarly journals Multistep Hybrid Extragradient Method for Triple Hierarchical Variational Inequalities

2013 ◽  
Vol 2013 ◽  
pp. 1-17 ◽  
Author(s):  
Zhao-Rong Kong ◽  
Lu-Chuan Ceng ◽  
Qamrul Hasan Ansari ◽  
Chin-Tzong Pang
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Variational Inequality Problem ◽  
Extragradient Method ◽  
Fixed Point Set ◽  
Inequality Problem ◽  
Hybrid Extragradient Method ◽  
Point Set ◽  
Hierarchical Variational Inequalities

We consider a triple hierarchical variational inequality problem (THVIP), that is, a variational inequality problem defined over the set of solutions of another variational inequality problem which is defined over the intersection of the fixed point set of a strict pseudocontractive mapping and the solution set of the classical variational inequality problem. Moreover, we propose a multistep hybrid extragradient method to compute the approximate solutions of the THVIP and present the convergence analysis of the sequence generated by the proposed method. We also derive a solution method for solving a system of hierarchical variational inequalities (SHVI), that is, a system of variational inequalities defined over the intersection of the fixed point set of a strict pseudocontractive mapping and the solution set of the classical variational inequality problem. Under very mild conditions, it is proven that the sequence generated by the proposed method converges strongly to a unique solution of the SHVI.

scholarly journals New algorithm method for solving the variational inequality problem in Hilbert space

2019 ◽  
Vol 7 (2) ◽  
pp. 15 ◽  
Author(s):  
Zena Hussein Maibed
Keyword(s):  
Hilbert Space ◽  
Variational Inequality ◽  
Variational Inequality Problem ◽  
Inequality Problem ◽  
Resolvent Mappings

Theipurpose of,thisipaper,is toiintroduce,aiconcept of generalizedinon_spreading,and define a new algorithm,for infinite,families of generalizedinon_spreading,and finite families of resolvent,mappings. Also, We study,the existence,solution of variational inequality,to a commonifixedipoint in Hilbertispaces. The main,results in this paper extendiand generalized,of many knowniresults initheiliterature.  

scholarly journals New Tseng-Degree Gradient Method in Variational Inequality Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Zhuang Shan ◽  
Lijun Zhu ◽  
Long He ◽  
Danfeng Wu ◽  
Haicheng Wei
Keyword(s):  
Hilbert Space ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
High Precision ◽  
Gradient Method ◽  
Variational Inequality Problem ◽  
Real Hilbert Space ◽  
Monotone Operators ◽  
Inequality Problem ◽  
Convergence Performance

This paper focuses on the problem of variational inequalities with monotone operators in real Hilbert space. The Tseng algorithm constructed by Thong replaced a high-precision step. Thus, a new Tseng-like gradient method is constructed, and the convergence of the algorithm is proved, and the convergence performance is higher.

scholarly journals New Tseng’s extragradient methods for pseudomonotone variational inequality problems in Hadamard manifolds

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Konrawut Khammahawong ◽  
Poom Kumam ◽  
Parin Chaipunya ◽  
Somyot Plubtieng
Keyword(s):  
Variational Inequality ◽  
Numerical Experiments ◽  
Vector Fields ◽  
Variational Inequality Problem ◽  
Variational Inequality Problems ◽  
Hadamard Manifolds ◽  
Extragradient Methods ◽  
Continuous Vector ◽  
Inequality Problem ◽  
Lipschitz Continuous

AbstractWe propose Tseng’s extragradient methods for finding a solution of variational inequality problems associated with pseudomonotone vector fields in Hadamard manifolds. Under standard assumptions such as pseudomonotone and Lipschitz continuous vector fields, we prove that any sequence generated by the proposed methods converges to a solution of variational inequality problem, whenever it exits. Moreover, we give some numerical experiments to illustrate our main results.

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