scholarly journals On the Convergence and O(1/N) Complexity of a Class of Nonlinear Proximal Point Algorithms for Monotonic Variational Inequalities

10.19139/73 ◽  
2014 ◽  
Vol 2 (2) ◽  
Author(s):  
Jian Wu ◽  
Gaohang Yu
Keyword(s):  
Variational Inequalities ◽  
Proximal Point ◽  
Proximal Point Algorithms

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.

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