scholarly journals A resolvent method for solving mixed variational inequalities

2011 ◽  
Vol 23 (2) ◽  
pp. 235-240
Author(s):  
Abdellah Bnouhachem ◽  
Muhammad Aslam Noor ◽  
Mohamed Khalfaoui ◽  
Sheng Zhaohan
Keyword(s):  
Variational Inequalities ◽  
Resolvent Method ◽  
Mixed Variational Inequalities

scholarly journals Some Proximal Methods for Solving Mixed Variational Inequalities

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Muhammad Aslam Noor ◽  
Zhenyu Huang
Keyword(s):  
Variational Inequalities ◽  
Extragradient Method ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Proximal Methods ◽  
Proximal Point ◽  
Equivalent Formulation ◽  
New Methods ◽  
Special Cases ◽  
Mixed Variational Inequalities

It is well known that the mixed variational inequalities are equivalent to the fixed point problem. We use this alternative equivalent formulation to suggest some new proximal point methods for solving the mixed variational inequalities. These new methods include the explicit, the implicit, and the extragradient method as special cases. The convergence analysis of these new methods is considered under some suitable conditions. Our method of constructing these iterative methods is very simple. Results proved in this paper may stimulate further research in this direction.

scholarly journals An Interior Projected-Like Subgradient Method for Mixed Variational Inequalities

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Guo-ji Tang ◽  
Xing Wang
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Subgradient Method ◽  
Mixed Variational Inequality ◽  
Convergence Estimate ◽  
Finite Dimensional ◽  
Mixed Variational Inequalities

An interior projected-like subgradient method for mixed variational inequalities is proposed in finite dimensional spaces, which is based on using non-Euclidean projection-like operator. Under suitable assumptions, we prove that the sequence generated by the proposed method converges to a solution of the mixed variational inequality. Moreover, we give the convergence estimate of the method. The results presented in this paper generalize some recent results given in the literatures.

Sign in / Sign up

Export Citation Format

Share Document