Weak Convergence Theorems for a Class of Split Variational Inequality Problems

2018 ◽  
Author(s):  
Kamonrat Sombut ◽  
Duangkamon Kitkuan ◽  
Anantachai Padcharoen ◽  
Poom Kumam
Keyword(s):  
Variational Inequality ◽  
Weak Convergence ◽  
Variational Inequality Problems ◽  
Convergence Theorems ◽  
Split Variational Inequality

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.

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