Modified extragradient methods for solving variational inequalities

In this paper, we propose two methods for solving variational inequalities. In the first method, we modified the extragradient method by using a new step size while the second method can be viewed as an extension of the first one by performing an additional projection step at each iteration and anot...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2009, Vol.57 (2), p.230-239
Main Authors: Bnouhachem, Abdellah, Xu, M.H., Fu, Xiao-Ling, Zhaohan, Sheng
Format: Article
Language:English
Subjects:
Computer simulation
Convergence
Extragradient methods
Inequalities
Iterative methods
Mathematical models
Monotone operators
Optimization
Prediction-correction methods
Projection
Projection methods
Self-adaptive rules
Variational inequalities
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Summary:In this paper, we propose two methods for solving variational inequalities. In the first method, we modified the extragradient method by using a new step size while the second method can be viewed as an extension of the first one by performing an additional projection step at each iteration and another optimal step length is employed to reach substantial progress in each iteration. Under certain conditions, the global convergence of two methods is proved. Preliminary numerical experiments are included to illustrate the efficiency of the proposed methods.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2008.10.065