Strong convergence of new iterative projection methods with regularization for solving monotone variational inequalities in Hilbert spaces

2020 ◽  
Vol 43 (17) ◽  
pp. 9745-9765 ◽  
Author(s):  
Dang Van Hieu ◽  
Le Dung Muu ◽  
Hoang Ngoc Duong ◽  
Buu Huu Thai
Keyword(s):  
Variational Inequalities ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Projection Methods ◽  
Monotone Variational Inequalities

scholarly journals Weak and strong convergence results for the modified Noor iteration of three quasi-nonexpansive multivalued mappings in Hilbert spaces

Filomat ◽  
2020 ◽  
Vol 34 (8) ◽  
pp. 2495-2510
Author(s):  
Watcharaporn Chaolamjiak ◽  
Suhel Khan ◽  
Hasanen Hammad ◽  
Hemen Dutta
Keyword(s):  
Strong Convergence ◽  
Hilbert Spaces ◽  
Projection Methods ◽  
Iteration Scheme ◽  
Multivalued Mappings ◽  
Technical Term ◽  
Convergence Results ◽  
Comparison Results ◽  
Weak Convergence Theorem ◽  
Shrinking Projection Methods

The paper aims to present an advanced algorithm by taking help of the Noor-iteration scheme along with the inertial technical term for three quasi-nonexpansive multivalued in Hilbert spaces. A weak convergence theorem under certain conditions has been given and added the CQ and shrinking projection methods to our algorithm to obtain certain strong convergence results. Furthermore, numerical experiments are provided by constructing an example and comparison results have also been incorporated.

scholarly journals New extragradient methods with non-convex combination for pseudomonotone equilibrium problems with applications in Hilbert spaces

Filomat ◽  
2019 ◽  
Vol 33 (6) ◽  
pp. 1677-1693 ◽  
Author(s):  
Shenghua Wang ◽  
Yifan Zhang ◽  
Ping Ping ◽  
Yeol Cho ◽  
Haichao Guo
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Fixed Point Theorems ◽  
Equilibrium Problems ◽  
Convex Combination ◽  
Projection Methods ◽  
Extragradient Methods ◽  
Numerical Examples

In the literature, the most authors modify the viscosity methods or hybrid projection methods to construct the strong convergence algorithms for solving the pseudomonotone equilibrium problems. In this paper, we introduce some new extragradient methods with non-convex combination to solve the pseudomonotone equilibrium problems in Hilbert space and prove the strong convergence for the constructed algorithms. Our algorithms are very different with the existing ones in the literatures. As the application, the fixed point theorems for strict pseudo-contraction are considered. Finally, some numerical examples are given to show the effectiveness of the algorithms.

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.

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