scholarly journals Projection-proximal methods for general variational inequalities

2006 ◽  
Vol 318 (1) ◽  
pp. 53-62 ◽  
Author(s):  
Muhammad Aslam Noor
Keyword(s):  
Variational Inequalities ◽  
Proximal Methods ◽  
General 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 Parametric Extended General Mixed Variational Inequalities

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Muhammad Aslam Noor
Keyword(s):  
Variational Inequalities ◽  
Complementarity Problems ◽  
Equivalent Formulation ◽  
Resolvent Equations ◽  
Special Cases ◽  
General Variational Inequalities ◽  
Significant Extension ◽  
Mixed Variational Inequalities ◽  
The Given

It is well known that the resolvent equations are equivalent to the extended general mixed variational inequalities. We use this alternative equivalent formulation to study the sensitivity of the extended general mixed variational inequalities without assuming the differentiability of the given data. Since the extended general mixed variational inequalities include extended general variational inequalities, quasi (mixed) variational inequalities and complementarity problems as special cases, results obtained in this paper continue to hold for these problems. In fact, our results can be considered as a significant extension of previously known results.

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