scholarly journals A modified projection method for monotone variational inequalities

1999 ◽  
Vol 12 (5) ◽  
pp. 83-87 ◽  
Author(s):  
M.A. Noor
Keyword(s):  
Variational Inequalities ◽  
Projection Method ◽  
Monotone Variational Inequalities ◽  
Modified Projection Method

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.

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