Mathematical Problems in Engineering
Volume 2008 (2008), Article ID 280956, 13 pages
On Self-Adaptive Method for General Mixed Variational Inequalities
1School of Management Science and Engineering, Nanjing University, Nanjing 210093, China
2Ibn Zohr University, Présidence, BP 32/S, 80000 Agadir, Morocco
3Mathematics Department, Faculty of Sciences, COMSATS Institute of Information Technology, Plot no. 30, Sector H-8, Islamabad, Pakistan
4Mathematics Department, College of Basic Education, Main Campus, Shamiyah, Adiliya 73251, Kuwait
Received 13 September 2007; Accepted 17 April 2008
Academic Editor: Alois Steindl
Copyright © 2008 Abdellah Bnouhachem et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We suggest and analyze a new self-adaptive method for solving general mixed variational inequalities, which can be viewed as an improvement of the method of (Noor 2003). Global convergence of the new method is proved under the same assumptions as Noor's method. Some preliminary computational results are given to illustrate the efficiency of the proposed method. Since the general mixed variational inequalities include general variational inequalities, quasivariational inequalities, and nonlinear (implicit) complementarity problems as special cases, results proved in this paper continue to hold for these problems.