Two new extragradient methods for solving equilibrium problems

2021 ◽  
Vol 115 (2) ◽  
Author(s):  
Habib ur Rehman ◽  
Aviv Gibali ◽  
Poom Kumam ◽  
Kanokwan Sitthithakerngkiet
Keyword(s):  
Equilibrium Problems ◽  
Extragradient Methods

Modified proximal-like extragradient methods for two classes of equilibrium problems in Hilbert spaces with applications

2021 ◽  
Vol 40 (2) ◽  
Author(s):  
Habib ur Rehman ◽  
Poom Kumam ◽  
Ioannis K. Argyros ◽  
Nasser Aedh Alreshidi
Keyword(s):  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Extragradient Methods

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.

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.

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.

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