- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 836720, 6 pages
A Projection-Type Method for Multivalued Variational Inequality
Institute of Applied Mathematics, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
Received 18 April 2013; Revised 5 August 2013; Accepted 19 August 2013
Academic Editor: Shawn X. Wang
Copyright © 2013 Changjie Fang 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.
- T. Q. Bao and P. Q. Khanh, “A projection-type algorithm for pseudomonotone nonlips-chitzian multivalued variational inequalities, in generalized convexity,generalized monotonicity and applications,” in Proceedings of the 7th International Symposium on Generalized Convexity and Generalized Monotonicity, A. Eberhard, N. Hadjisavvas, and D. T. Lus, Eds., pp. 113–129, Springer, 2005.
- Y. Censor, A. Gibali, and S. Reich, “Extensions of Korpelevich's extragradient method for the variational inequality problem in Euclidean space,” Optimization, vol. 61, no. 9, pp. 1119–1132, 2012.
- F. Facchinei and J.-S. Pang, Finite-Dimensional Variational Inequalities and Complementary Problems, Springer, New York, NY, USA, 2003.
- Y. He, “A new double projection algorithm for variational inequalities,” Journal of Computational and Applied Mathematics, vol. 185, no. 1, pp. 166–173, 2006.
- F. Li and Y. He, “An algorithm for generalized variational inequality with pseudomonotone mapping,” Journal of Computational and Applied Mathematics, vol. 228, no. 1, pp. 212–218, 2009.
- M. V. Solodov and B. F. Svaiter, “A new projection method for variational inequality problems,” SIAM Journal on Control and Optimization, vol. 37, no. 3, pp. 765–776, 1999.
- D. Sun, “A class of iterative methods for solving nonlinear projection equations,” Journal of Optimization Theory and Applications, vol. 91, no. 1, pp. 123–140, 1996.
- 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.
- 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.
- 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.
- H. Chen, “A new extragradient method for generalized variational inequality in Euclidean space,” Fixed Point Theory and Applications, vol. 2013, article 139, 2013.
- 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.
- S. C. Fang and E. L. Peterson, “Generalized variational inequalities,” Journal of Optimization Theory and Applications, vol. 38, no. 3, pp. 363–383, 1982.
- M. Fukushima, “The primal Douglas-Rachford splitting algorithm for a class of monotone mappings with application to the traffic equilibrium problem,” Mathematical Programming A, vol. 72, no. 1, pp. 1–15, 1996.
- Y. He, “Stable pseudomonotone variational inequality in reflexive Banach spaces,” Journal of Mathematical Analysis and Applications, vol. 330, no. 1, pp. 352–363, 2007.
- R. Saigal, “Extension of the generalized complementarity problem,” Mathematics of Operations Research, vol. 1, no. 3, pp. 260–266, 1976.
- G. Salmon, J.-J. Strodiot, and V. H. Nguyen, “A bundle method for solving variational inequalities,” SIAM Journal on Optimization, vol. 14, no. 3, pp. 869–893, 2003.
- M. V. Solodov and B. F. Svaiter, “Forcing strong convergence of proximal point iterations in a Hilbert space,” Mathematical Programming A, vol. 87, no. 1, pp. 189–202, 2000.
- R. T. Rockafellar, “Monotone operators and the proximal point algorithm,” SIAM Journal on Control and Optimization, vol. 14, no. 5, pp. 877–898, 1976.
- I. V. Konnov, “On the rate of convergence of combined relaxation methods,” Izvestiya Vysshikh Uchebnykh Zavedeniĭ. Matematika, vol. 37, no. 12, pp. 89–92, 1993.
- I. V. Konnov, Combined Relaxation Methods for Variational Inequalities, Springer, Berlin, Germany, 2001.
- C. J. Fang and Y. R. He, “An extragradient method for generalized variational inequality,” Pacic Journal of Optimization, vol. 9, no. 1, pp. 47–59, 2013.
- C. J. Fang, S. L. Chen, and C. D. Yang, “An algorithm for solving multi-valued variational inequality,” Journal of Inequalities and Applications, vol. 2013, article 218, 2013.
- S. Karamardian, “Complementarity problems over cones with monotone and pseudomonotone maps,” Journal of Optimization Theory and Applications, vol. 18, no. 4, pp. 445–454, 1976.
- E. H. Zarantonello, “Projections on convex sets in Hilbert space and spectral theory,” in Contributions to Nonlinear Functional Analysis, E. H. Zarantonello, Ed., Academic Press, New York, NY, USA, 1971.
- J.-P. Aubin and I. Ekeland, Applied Nonlinear Analysis, John Wiley & Sons, New Yor, NY, USA, 1984.