Modified inertial subgradient extragradient method for equilibrium problems

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Lateef Olakunle Jolaoso ◽  
Yekini Shehu ◽  
Regina N. Nwokoye
Keyword(s):  
Variational Inequalities ◽  
Strong Convergence ◽  
Equilibrium Problems ◽  
Extragradient Method ◽  
Subgradient Extragradient Method ◽  
Weak And Strong Convergence ◽  
Extragradient Methods ◽  
Convergence Results ◽  
Inertial Extrapolation ◽  
Special Case

Abstract The subgradient extragradient method with inertial extrapolation step x n + θ n (x n − x n−1) (also known as inertial subgradient extragradient method) has been studied extensively in the literature for solving variational inequalities and equilibrium problems. Most of the inertial subgradient extragradient methods in the literature for both variational inequalities and equilibrium problems have not considered the special case when the inertial factor θ n = 1. The convergence results have always been obtained when the inertial factor θ n is assumed 0 ≤ θ n < 1. This paper considers the relaxed inertial version of subgradient extragradient method for equilibrium problems with 0 ≤ θ n ≤ 1. We give both weak and strong convergence results using this inertial subgradient extragradient method and also give some numerical illustrations.

scholarly journals Extended Extragradient Methods for Generalized Variational Inequalities

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Yonghong Yao ◽  
Yeong-Cheng Liou ◽  
Cun-Lin Li ◽  
Hui-To Lin
Keyword(s):  
Banach Space ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Extragradient Method ◽  
Extragradient Methods ◽  
Generalized Variational Inequalities ◽  
Mild Conditions ◽  
Convergence Results ◽  
Special Cases

We suggest a modified extragradient method for solving the generalized variational inequalities in a Banach space. We prove some strong convergence results under some mild conditions on parameters. Some special cases are also discussed.

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 Variational Inequalities Approaches to Minimization Problems with Constraints of Generalized Mixed Equilibria and Variational Inclusions

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 270 ◽  
Author(s):  
Lu-Chuan Ceng ◽  
Mihai Postolache ◽  
Ching-Feng Wen ◽  
Yonghong Yao
Keyword(s):  
Variational Inequalities ◽  
Strong Convergence ◽  
Equilibrium Problems ◽  
Variational Inclusions ◽  
Minimization Problems ◽  
Convergence Results ◽  
Mixed Equilibrium Problems ◽  
Generalized Mixed Equilibrium ◽  
Implicit And Explicit ◽  
Mixed Equilibria

Multistep composite implicit and explicit extragradient-like schemes are presented for solving the minimization problem with the constraints of variational inclusions and generalized mixed equilibrium problems. Strong convergence results of introduced schemes are given under suitable control conditions.

scholarly journals Inertial Extragradient Methods for Solving Split Equilibrium Problems

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1884
Author(s):  
Suthep Suantai ◽  
Narin Petrot ◽  
Manatchanok Khonchaliew
Keyword(s):  
Strong Convergence ◽  
Hilbert Spaces ◽  
Numerical Experiments ◽  
Equilibrium Problems ◽  
Constraint Qualifications ◽  
Weak And Strong Convergence ◽  
Convergence Theorems ◽  
Extragradient Methods

This paper presents two inertial extragradient algorithms for finding a solution of split pseudomonotone equilibrium problems in the setting of real Hilbert spaces. The weak and strong convergence theorems of the introduced algorithms are presented under some constraint qualifications of the scalar sequences. The discussions on the numerical experiments are also provided to demonstrate the effectiveness of the proposed algorithms.

scholarly journals A strong convergence theorem for solving pseudo-monotone variational inequalities and fixed point problems using subgradient extragradient method in Banach spaces

2021 ◽  
Vol 7 (4) ◽  
pp. 5015-5028
Author(s):  
Fei Ma ◽  
◽  
Jun Yang ◽  
Min Yin
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Extragradient Method ◽  
Lipschitz Constant ◽  
Fixed Point Problems ◽  
Strong Convergence Theorem ◽  
Subgradient Extragradient Method ◽  
Step Size ◽  
Common Solution

<abstract><p>In this paper, we introduce an algorithm for solving variational inequalities problem with Lipschitz continuous and pseudomonotone mapping in Banach space. We modify the subgradient extragradient method with a new and simple iterative step size, and the strong convergence to a common solution of the variational inequalities and fixed point problems is established without the knowledge of the Lipschitz constant. Finally, a numerical experiment is given in support of our results.</p></abstract>

scholarly journals Analysis of Subgradient Extragradient Iterative Schemes for Variational Inequalities

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Danfeng Wu ◽  
Li-Jun Zhu ◽  
Zhuang Shan ◽  
Tzu-Chien Yin
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Convergence Analysis ◽  
Hilbert Spaces ◽  
Extragradient Method ◽  
Subgradient Extragradient Method ◽  
Iterative Schemes ◽  
Mild Conditions ◽  
Monotone Variational Inequality

In this paper, we investigate the monotone variational inequality in Hilbert spaces. Based on Censor’s subgradient extragradient method, we propose two modified subgradient extragradient algorithms with self-adaptive and inertial techniques for finding the solution of the monotone variational inequality in real Hilbert spaces. Strong convergence analysis of the proposed algorithms have been obtained under some mild conditions.

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