Table of Contents
ISRN Mathematical Analysis
Volume 2013 (2013), Article ID 727892, 8 pages
http://dx.doi.org/10.1155/2013/727892
Research Article

An Improved Two-Step Method for Generalized Variational Inequalities

School of Management Science, Qufu Normal University, Rizhao, Shandong 276800, China

Received 22 July 2013; Accepted 30 August 2013

Academic Editors: R. D. Chen and Y. Dai

Copyright © 2013 Haibin Chen. 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. Auslender and M. Teboulle, “Lagrangian duality and related multiplier methods for variational inequality problems,” SIAM Journal on Optimization, vol. 10, no. 4, pp. 1097–1115, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  2. Y. Censor, A. Gibali, and S. Reich, “The subgradient extragradient method for solving variational inequalities in Hilbert space,” Journal of Optimization Theory and Applications, vol. 148, no. 2, pp. 318–335, 2011. View at Publisher · View at Google Scholar · 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 MathSciNet
  4. Y. J. Wang, N. H. Xiu, and J. Z. Zhang, “Modified extragradient method for variational inequalities and verification of solution existence,” Journal of Optimization Theory and Applications, vol. 119, no. 1, pp. 167–183, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  5. A. Ben-Tal and A. Nemirovski, “Robust convex optimization,” Mathematics of Operations Research, vol. 23, no. 4, pp. 769–805, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  6. F. Facchinei and J. S. Pang, Finite Dimensional Variational Inequalities and Complementarity Problems, Springer, New York, NY, USA, 2003.
  7. C. Fang and Y. He, “A double projection algorithm for multi-valued variational inequalities and a unified framework of the method,” Applied Mathematics and Computation, vol. 217, no. 23, pp. 9543–9551, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  8. Y. He, “Stable pseudomonotone variational inequality in reflexive Banach spaces,” Journal of Mathematical Analysis and Applications, vol. 330, no. 1, pp. 352–363, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  9. N.-J. Huang, “Generalized nonlinear variational inclusions with noncompact valued mappings,” Applied Mathematics Letters, vol. 9, no. 3, pp. 25–29, 1996. View at Publisher · View at Google Scholar · View at MathSciNet
  10. S. Li and G. Chen, “On relations between multiclass, multicriteria traffic network equilibrium models and vector variational inequalities,” Journal of Systems Science and Systems Engineering, vol. 15, no. 3, pp. 284–297, 2006. View at Publisher · View at Google Scholar · View at Scopus
  11. R. Saigal, “Extension of the generalized complementarity problem,” Mathematics of Operations Research, vol. 1, no. 3, pp. 260–266, 1976. View at Publisher · View at Google Scholar · View at MathSciNet
  12. Y. He, “The Tikhonov regularization method for set-valued variational inequalities,” Abstract and Applied Analysis, vol. 2012, Article ID 172061, 10 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  13. G. M. Korpelevich, “An extragradient method for finding saddle points and for other problems,” Matecon, vol. 12, no. 4, pp. 747–756, 1976. View at Google Scholar · View at MathSciNet
  14. E. Allevi, A. Gnudi, and I. V. Konnov, “The proximal point method for nonmonotone variational inequalities,” Mathematical Methods of Operations Research, vol. 63, no. 3, pp. 553–565, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  15. 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 MathSciNet
  16. B. T. Polyak, Introduction to Optimization, Optimization Software Incorporation, Publications Division, New York, NY, USA, 1987. View at MathSciNet
  17. D. Kinderlehrer and G. Stampacchia, An Introduction to Variational Inequalities and Their Applications, Academic Press, New York, NY, USA, 1980. View at MathSciNet
  18. J.-P. Aubin and I. Ekeland, Applied Nonlinear Analysis, John Wiley & Sons, New York, NY, USA, 1984. View at MathSciNet
  19. Y. He, “A new double projection algorithm for variational inequalities,” Journal of Computational and Applied Mathematics, vol. 185, no. 1, pp. 166–173, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  20. M. V. Solodov, “Convergence rate analysis of iteractive algorithms for solving variational inquality problems,” Mathematical Programming, vol. 96, no. 3, pp. 513–528, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  21. J. S. Pang, “Error bounds in mathematical programming,” Mathematical Programming, vol. 79, no. 1–3, pp. 299–332, 1997. View at Google Scholar
  22. F.-Q. Xia and N.-J. Huang, “A projection-proximal point algorithm for solving generalized variational inequalities,” Journal of Optimization Theory and Applications, vol. 150, no. 1, pp. 98–117, 2011. View at Publisher · View at Google Scholar · View at MathSciNet