Modified extragradient methods for solving variational inequalities

Authors:
Abdellah Bnouhachem;M. H. Xu;Xiao-Ling Fu;Sheng Zhaohan
Affiliations:
School of Management Science and Engineering, Nanjing University, Nanjing, 210093, PR China and Ibn Zohr University, ENSA, BP 32/S, Agadir, Morocco;Department of Information Science, Jiangsu Polytechnic University, Chanzhou, Jiangsu Province, 213016, PR China;Department of Mathematics, Nanjing University, Nanjing, 210093, PR China;School of Management Science and Engineering, Nanjing University, Nanjing, 210093, PR China
Venue:
Computers & Mathematics with Applications
Year:
2009

Citing 12
Cited 0

Projected gradient methods for linearly constrained problems

Mathematical Programming: Series A and B
Modification of the extra-gradient method for solving variational inequalities and certain optimization problems

USSR Computational Mathematics and Mathematical Physics
A globally convergent Newton method for solving strongly monotone variational inequalities

Mathematical Programming: Series A and B
On linear convergence of iterative methods for the variational inequality problem

Proceedings of the international meeting on Linear/nonlinear iterative methods and verification of solution
Modified Projection-Type Methods for Monotone Variational Inequalities

SIAM Journal on Control and Optimization
A class of iterative methods for solving nonlinear projection equations

Journal of Optimization Theory and Applications
Improvements of some projection methods for monotone nonlinear variational inequalities

Journal of Optimization Theory and Applications
Modified Goldstein-Levitin-Polyak projection method for asymmetric strongly monotone variational inequalities

Journal of Optimization Theory and Applications
Local convergence analysis of projection-type algorithms: unified approach

Journal of Optimization Theory and Applications
Comparison of Two Kinds of Prediction-Correction Methods for Monotone Variational Inequalities

Computational Optimization and Applications
Interior projection-like methods for monotone variational inequalities

Mathematical Programming: Series A and B
A note on a globally convergent Newton method for solving monotone variational inequalities

Operations Research Letters

Quantified Score

Hi-index	0.09

Visualization

Abstract

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.