scholarly journals Iteration-Complexity of a Newton Proximal Extragradient Method for Monotone Variational Inequalities and Inclusion Problems

2012 ◽  
Vol 22 (3) ◽  
pp. 914-935 ◽  
Author(s):  
Renato D. C. Monteiro ◽  
Benar F. Svaiter
Keyword(s):  
Variational Inequalities ◽  
Extragradient Method ◽  
Iteration Complexity ◽  
Monotone Variational Inequalities ◽  
Inclusion Problems

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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