scholarly journals New linear convergence results on quasi-variational inequalities

2021 ◽  
Vol 3 (3) ◽  
Keyword(s):  
Variational Inequalities ◽  
Linear Convergence ◽  
Convergence Results

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.

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 Solving Composite Fixed Point Problems with Block Updates

2021 ◽  
Vol 10 (1) ◽  
pp. 1154-1177
Author(s):  
Patrick L. Combettes ◽  
Lilian E. Glaudin
Keyword(s):  
Fixed Point ◽  
Nonsmooth Analysis ◽  
Data Science ◽  
Linear Convergence ◽  
Common Fixed Points ◽  
Fixed Point Problems ◽  
Monotone Inclusions ◽  
Minimization Problems ◽  
Convergence Results ◽  
Nonexpansive Operators

Abstract Various strategies are available to construct iteratively a common fixed point of nonexpansive operators by activating only a block of operators at each iteration. In the more challenging class of composite fixed point problems involving operators that do not share common fixed points, current methods require the activation of all the operators at each iteration, and the question of maintaining convergence while updating only blocks of operators is open. We propose a method that achieves this goal and analyze its asymptotic behavior. Weak, strong, and linear convergence results are established by exploiting a connection with the theory of concentrating arrays. Applications to several nonlinear and nonsmooth analysis problems are presented, ranging from monotone inclusions and inconsistent feasibility problems, to variational inequalities and minimization problems arising in data science.

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.

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