scholarly journals A self-adaptive projection method with improved step-size for solving variational inequalities

2008 ◽  
Vol 55 (4) ◽  
pp. 819-832 ◽  
Author(s):  
Xihong Yan ◽  
Deren Han ◽  
Wenyu Sun
Keyword(s):  
Variational Inequalities ◽  
Projection Method ◽  
Step Size ◽  
Self Adaptive

scholarly journals A self-adaptive projection method for a class of variant variational inequalities

2011 ◽  
pp. 117-129
Author(s):  
Abdellah Bnouhachem ◽  
Muhammad Aslam Noor ◽  
Mohamed Khalfaoui ◽  
Sheng Zhaohan
Keyword(s):  
Variational Inequalities ◽  
Projection Method ◽  
Self Adaptive

Self-adaptive projection method for co-coercive variational inequalities

2009 ◽  
Vol 196 (1) ◽  
pp. 43-48 ◽  
Author(s):  
Bingsheng He ◽  
Xiao-Zheng He ◽  
Henry X. Liu ◽  
Ting Wu
Keyword(s):  
Variational Inequalities ◽  
Projection Method ◽  
Self Adaptive

MODIFIED PROJECTION METHOD FOR GENERAL VARIATIONAL INEQUALITIES

2011 ◽  
Vol 25 (27) ◽  
pp. 3595-3610 ◽  
Author(s):  
ABDELLAH BNOUHACHEM ◽  
MUHAMMAD ASLAM NOOR ◽  
ZHAOHAN SHENG
Keyword(s):  
Global Convergence ◽  
Variational Inequalities ◽  
Projection Method ◽  
Complementarity Problems ◽  
Descent Direction ◽  
Step Size ◽  
Special Cases ◽  
General Variational Inequalities ◽  
Modified Projection Method

In this paper, we suggest and analyze a modified descent-projection method for solving general variational inequalities. The method makes use of a descent direction to produce the new iterate and can be viewed as an improvement of the descent-projection method by using a new step size. We also prove the global convergence of the proposed method. An example is given to illustrate the efficiency and its comparison with other methods. Since the general variational inequalities include quasi variational inequalities and implicit complementarity problems as special cases, results proved in this paper continue to hold for these problems.

scholarly journals A Self-Adaptive Method for Solving a System of Nonlinear Variational Inequalities

2007 ◽  
Vol 2007 ◽  
pp. 1-7
Author(s):  
Chaofeng Shi
Keyword(s):  
Iterative Method ◽  
Variational Inequalities ◽  
Adaptive Method ◽  
New Method ◽  
Computational Results ◽  
Computation Cost ◽  
Self Adaptive

The system of nonlinear variational inequalities (SNVI) is a useful generalization of variational inequalities. Verma (2001) suggested and analyzed an iterative method for solving SNVI. In this paper, we present a new self-adaptive method, whose computation cost is less than that of Verma's method. The convergence of the new method is proved under the same assumptions as Verma's method. Some preliminary computational results are given to illustrate the efficiency of the proposed method.

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