scholarly journals The convergence analysis of the projection methods for a system of generalized relaxed cocoercive variational inequalities in Hilbert spaces

2013 ◽  
Vol 2013 (1) ◽  
Author(s):  
Yifen Ke ◽  
Changfeng Ma
Keyword(s):  
Variational Inequalities ◽  
Convergence Analysis ◽  
Hilbert Spaces ◽  
Projection Methods

scholarly journals Iterative Algorithms for Pseudomonotone Variational Inequalities and Fixed Point Problems of Pseudocontractive Operators

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1189 ◽  
Author(s):  
Yonghong Yao ◽  
Mihai Postolache ◽  
Jen-Chih Yao
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Convergence Analysis ◽  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Iterative Algorithms ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Common Solution

In this paper, we are interested in the pseudomonotone variational inequalities and fixed point problem of pseudocontractive operators in Hilbert spaces. An iterative algorithm has been constructed for finding a common solution of the pseudomonotone variational inequalities and fixed point of pseudocontractive operators. Strong convergence analysis of the proposed procedure is given. Several related corollaries are included.

Generalized System for Relaxed Cocoercive and Involving Projective Nonexpansive Mapping Variational Inequalities

2011 ◽  
Vol 393-395 ◽  
pp. 792-795
Author(s):  
Guang Hui Gu ◽  
Yong Fu Su
Keyword(s):  
Variational Inequalities ◽  
Nonexpansive Mapping ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Projection Methods ◽  
Generalized System

Firstly, the concept of projective nonexpansive mappings is presented in this paper. The approximate solvability of a generalized system for relaxed cocoercive and involving projective nonexpansive mapping nonlinear variational inequalities in Hilbert spaces is studied, based on the convergence of projection methods. The results presented in this paper extend and improve the main results of many authors.

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.

scholarly journals Convergence of Some Iterative Algorithms for System of Generalized Set-Valued Variational Inequalities

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
M. Akram ◽  
Aysha Khan ◽  
M. Dilshad
Keyword(s):  
Variational Inequalities ◽  
Strong Convergence ◽  
Convergence Analysis ◽  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Iterative Algorithms ◽  
Existence Of A Solution ◽  
Banach Contraction ◽  
Parallel Iterative Algorithms ◽  
Parallel Iterative

In this article, we consider and study a system of generalized set-valued variational inequalities involving relaxed cocoercive mappings in Hilbert spaces. Using the projection method and Banach contraction principle, we prove the existence of a solution for the considered problem. Further, we propose an iterative algorithm and discuss its convergence. Moreover, we establish equivalence between the system of variational inequalities and altering points problem. Some parallel iterative algorithms are proposed, and the strong convergence of the sequences generated by these iterative algorithms is discussed. Finally, a numerical example is constructed to illustrate the convergence analysis of the proposed parallel iterative algorithms.

scholarly journals A Forward-Backward-Forward Algorithm for Solving Quasimonotone Variational Inequalities

2022 ◽  
Vol 2022 ◽  
pp. 1-8
Author(s):  
Tzu-Chien Yin ◽  
Nawab Hussain
Keyword(s):  
Variational Inequalities ◽  
Convergence Analysis ◽  
Prior Knowledge ◽  
Hilbert Spaces ◽  
Lipschitz Constant ◽  
Weak Continuity ◽  
Forward Algorithm ◽  
Adaptive Technique ◽  
Quasimonotone Operators ◽  
Self Adaptive

In this paper, we continue to investigate the convergence analysis of Tseng-type forward-backward-forward algorithms for solving quasimonotone variational inequalities in Hilbert spaces. We use a self-adaptive technique to update the step sizes without prior knowledge of the Lipschitz constant of quasimonotone operators. Furthermore, we weaken the sequential weak continuity of quasimonotone operators to a weaker condition. Under some mild assumptions, we prove that Tseng-type forward-backward-forward algorithm converges weakly to a solution of quasimonotone variational inequalities.

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