Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2007, Article ID 23795, 7 pages
http://dx.doi.org/10.1155/2007/23795
Research Article

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

1School of Mathematics, Sichuan University, Chengdou, Sichuan 610064, China
2Department of Mathematics, Xianyang Normal College, Xianyang, Shaanxi 712000, China

Received 24 April 2006; Accepted 9 March 2007

Academic Editor: A. Isidori

Copyright © 2007 Chaofeng Shi. 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.

Linked References

  1. A. Bnouhachem, “A self-adaptive method for solving general mixed variational inequalities,” Journal of Mathematical Analysis and Applications, vol. 309, no. 1, pp. 136–150, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. R. Glowinski, J.-L. Lions, and R. Trémolières, Numerical Analysis of Variational Inequalities, vol. 8 of Studies in Mathematics and Its Applications, North-Holland, Amsterdam, The Netherlands, 1981. View at Zentralblatt MATH · View at MathSciNet
  3. P. T. Harker and J.-S. Pang, “Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications,” Mathematical Programming, vol. 48, no. 2, pp. 161–220, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. B. S. He, “Inexact implicit methods for monotone general variational inequalities,” Mathematical Programming, vol. 86, no. 1, pp. 199–217, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. B. S. He and L. Z. Liao, “Improvements of some projection methods for monotone nonlinear variational inequalities,” Journal of Optimization Theory and Applications, vol. 112, no. 1, pp. 111–128, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. A. N. Iusem and B. F. Svaiter, “A variant of Korpelevich's method for variational inequalities with a new search strategy,” Optimization, vol. 42, no. 4, pp. 309–321, 1997. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. J.-L. Lions and G. Stampacchia, “Variational inequalities,” Communications on Pure and Applied Mathematics, vol. 20, pp. 493–519, 1967. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. C. Shi, S. Y. Liu, J. L. Lian, and B. D. Fang, “A modified prediction-correction method for a general monotone variational inequality,” Mathematica Numerica Sinica, vol. 27, no. 2, pp. 113–120, 2005. View at Google Scholar · View at MathSciNet
  9. R. U. Verma, “A class of quasivariational inequalities involving cocoercive mappings,” Advances in Nonlinear Variational Inequalities, vol. 2, no. 2, pp. 1–12, 1999. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. R. U. Verma, “An extension of a class of nonlinear quasivariational inequality problems based on a projection method,” Mathematical Sciences Research Hot-Line, vol. 3, no. 5, pp. 1–10, 1999. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. R. U. Verma, “Projection methods, algorithms, and a new system of nonlinear variational inequalities,” Computers & Mathematics with Applications, vol. 41, no. 7-8, pp. 1025–1031, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. Y. J. Wang, N. H. Xiu, and C. Y. Wang, “Unified framework of extragradient-type methods for pseudomonotone variational inequalities,” Journal of Optimization Theory and Applications, vol. 111, no. 3, pp. 641–656, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. Y. J. Wang, N. H. Xiu, and C. Y. Wang, “A new version of extragradient method for variational inequality problems,” Computers & Mathematics with Applications, vol. 42, no. 6-7, pp. 969–979, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet