- 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 2012 (2012), Article ID 768272, 10 pages
Iterative Algorithms for General Multivalued Variational Inequalities
1Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China
2Mathematics Department, College of Science, King Saud University, Riyadh 1145, Saudi Arabia
3Mathematics Department, COMSATS Institute of Information Technology, Islamabad 44000, Pakistan
4Department of Information Management, Cheng Shiu University, Kaohsiung 833, Taiwan
5Department of Mathematics and RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea
Received 21 October 2011; Accepted 1 November 2011
Academic Editor: Khalida Inayat Noor
Copyright © 2012 Yonghong Yao 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.
- L. C. Ceng, Q. H. Ansari, and J. C. Yao, “Relaxed extragradient iterative methods for variational inequalities,” Applied Mathematics and Computation, vol. 218, no. 3, pp. 1112–1123, 2011.
- L. C. Ceng, M. Teboulle, and J. C. Yao, “Weak convergence of an iterative method for pseudomonotone variational inequalities and fixed-point problems,” Journal of Optimization Theory and Applications, vol. 146, no. 1, pp. 19–31, 2010.
- S. S. Chang, H. W. J. Lee, C. K. Chan, and J. A. Liu, “A new method for solving a system of generalized nonlinear variational inequalities in Banach spaces,” Applied Mathematics and Computation, vol. 217, no. 16, pp. 6830–6837, 2011.
- F. Cianciaruso, G. Marino, L. Muglia, and Y. Yao, “On a two-step algorithm for hierarchical fixed point problems and variational inequalities,” Journal of Inequalities and Applications, vol. 2009, Article ID 208692, 13 pages, 2009.
- F. Facchinei and J. S. Pang, Finite-Dimensional Variational Inequalities and Complementarity Problems, vol. 1-2 of Springer Series in Operations Research, Springer, New York, NY, USA, 2003.
- R. Glowinski, Numerical Methods for Nonlinear Variational Problems, Springer, New York, 1984.
- B. S. He, “A new method for a class of linear variational inequalities,” Mathematical Programming, vol. 66, no. 2, pp. 137–144, 1994.
- 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.
- P. Jaillet, D. Lamberton, and B. Lapeyre, “Variational inequalities and the pricing of American options,” Acta Applicandae Mathematicae, vol. 21, no. 3, pp. 263–289, 1990.
- E. N. Khobotov, “Modification of the extra-gradient method for solving variational inequalities and certain optimization problems,” USSR Computational Mathematics and Mathematical Physics, vol. 27, no. 5, pp. 120–127, 1987.
- G. M. Korpelevich, “An extragradient method for finding saddle points and for other problems,” Ekonomika i Matematicheskie Metody, vol. 12, no. 4, pp. 747–756, 1976.
- P. Kumam, N. Petrot, and R. Wangkeeree, “Existence and iterative approximation of solutions of generalized mixed quasi-variational-like inequality problem in Banach spaces,” Applied Mathematics and Computation, vol. 217, no. 18, pp. 7496–7503, 2011.
- X. Lu, H. K. Xu, and X. Yin, “Hybrid methods for a class of monotone variational inequalities,” Nonlinear Analysis. Theory, Methods & Applications, vol. 71, no. 3-4, pp. 1032–1041, 2009.
- G. Marino, L. Muglia, and Y. Yao, “Viscosity methods for common solutions of equilibrium and variational inequality problems via multi-step iterative algorithms and common fixed points,” Nonlinear Analysis, Theory, Methods and Applications. In press.
- M. A. Noor, On Variational Inequalities, Brunel University, London, UK, 1975.
- M. A. Noor, “General variational inequalities,” Applied Mathematics Letters, vol. 1, no. 2, pp. 119–122, 1988.
- M. A. Noor, “Wiener-Hopf equations and variational inequalities,” Journal of Optimization Theory and Applications, vol. 79, no. 1, pp. 197–206, 1993.
- M. A. Noor, “Some developments in general variational inequalities,” Applied Mathematics and Computation, vol. 152, no. 1, pp. 199–277, 2004.
- M. A. Noor, “Differentiable non-convex functions and general variational inequalities,” Applied Mathematics and Computation, vol. 199, no. 2, pp. 623–630, 2008.
- M. A. Noor and E. A. Al-Said, “Wiener-Hopf equations technique for quasimonotone variational inequalities,” Journal of Optimization Theory and Applications, vol. 103, no. 3, pp. 705–714, 1999.
- M. A. Noor and Z. Huang, “Wiener-Hopf equation technique for variational inequalities and nonexpansive mappings,” Applied Mathematics and Computation, vol. 191, no. 2, pp. 504–510, 2007.
- P. Shi, “Equivalence of variational inequalities with Wiener-Hopf equations,” Proceedings of the American Mathematical Society, vol. 111, no. 2, pp. 339–346, 1991.
- 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.
- G. Stampacchia, “Formes bilineaires coercitives sur les ensembles convexes,” Comptes Rendus de l'Academie des Sciences, vol. 258, pp. 4413–4416, 1964.
- 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.
- H. K. Xu and T. H. Kim, “Convergence of hybrid steepest-descent methods for variational inequalities,” Journal of Optimization Theory and Applications, vol. 119, no. 1, pp. 185–201, 2003.
- J. C. Yao, “Variational inequalities with generalized monotone operators,” Mathematics of Operations Research, vol. 19, no. 3, pp. 691–705, 1994.
- Y. Yao, R. Chen, and H. K. Xu, “Schemes for finding minimum-norm solutions of variational inequalities,” Nonlinear Analysis. Theory, Methods & Applications, vol. 72, no. 7-8, pp. 3447–3456, 2010.
- Y. Yao, Y. C. Liou, and S. M. Kang, “Two-step projection methods for a system of variational inequality problems in Banach spaces,” Journal of Global Optimization. In press.
- Y. Yao, M. A. Noor, and Y. C. Liou, “Strong convergence of a modified extra-gradient method to the 4 minimum-norm solution of variational inequalities,” Abstract and Applied Analysis, vol. 2012, Article ID 817436, 9 pages, 2012.
- Y. Yao, M. A. Noor, K. I. Noor, Y. C. Liou, and H. Yaqoob, “Modified extragradient methods for a system of variational inequalities in Banach spaces,” Acta Applicandae Mathematicae, vol. 110, no. 3, pp. 1211–1224, 2010.
- Y. Yao and N. Shahzad, “New methods with perturbations for non-expansive mappings in Hilbert 5 spaces,” Fixed Point Theory and Applications, vol. 2011, Article ID 79, 2011.
- Y. Yao and N. Shahzad, “Strong convergence of a proximal point algorithm with general errors,” Optimization Letters. In press.