scholarly journals A Note On the Weak Convergence of the Extragradient Method for Solving Pseudo-Monotone Variational Inequalities

2020 ◽  
Vol 185 (1) ◽  
pp. 300-301
Author(s):  
Phan Tu Vuong
Keyword(s):  
Weak Convergence ◽  
Variational Inequalities ◽  
Extragradient Method ◽  
Monotone Variational Inequalities

scholarly journals Modified Viscosity Subgradient Extragradient-Like Algorithms for Solving Monotone Variational Inequalities Problems

Axioms ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 118 ◽  
Author(s):  
Nopparat Wairojjana ◽  
Mudasir Younis ◽  
Habib ur Rehman ◽  
Nuttapol Pakkaranang ◽  
Nattawut Pholasa
Keyword(s):  
Variational Inequalities ◽  
State Of The Art ◽  
Real Hilbert Space ◽  
Extragradient Method ◽  
Lipschitz Constant ◽  
Mathematical Optimization ◽  
Test Problems ◽  
Monotone Variational Inequalities ◽  
Engineering Economics ◽  
Inequality Theory

Variational inequality theory is an effective tool for engineering, economics, transport and mathematical optimization. Some of the approaches used to resolve variational inequalities usually involve iterative techniques. In this article, we introduce a new modified viscosity-type extragradient method to solve monotone variational inequalities problems in real Hilbert space. The result of the strong convergence of the method is well established without the information of the operator’s Lipschitz constant. There are proper mathematical studies relating our newly designed method to the currently state of the art on several practical test problems.

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