- 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 750473, 8 pages
Synchronal Algorithm and Cyclic Algorithm for Hierarchical Fixed Point Problems and Variational Inequalities
College of Science, Civil Aviation University of China, Tianjin 300300, China
Received 26 May 2013; Accepted 23 August 2013
Academic Editor: Sehie Park
Copyright © 2013 Peichao Duan. 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.
- P. L. Combettes, “A block-iterative surrogate constraint splitting method for quadratic signal recovery,” IEEE Transactions on Signal Processing, vol. 51, no. 7, pp. 1771–1782, 2003.
- H. Iiduka and I. Yamada, “A use of conjugate gradient direction for the convex optimization problem over the fixed point set of a nonexpansive mapping,” SIAM Journal on Optimization, vol. 19, no. 4, pp. 1881–1893, 2008.
- H. Iiduka, “Fixed point optimization algorithm and its application to power control in CDMA data networks,” Mathematical Programming, vol. 133, no. 1-2, pp. 227–242, 2012.
- L. C. Ceng, Q. H. Ansari, N. C. Wong, and J. C. Yao, “Implicit iterative method for hierarchical variational inequalities,” Journal of Applied Mathematics, vol. 2012, Article ID 472935, 14 pages, 2012.
- L. C. Ceng, Q. H. Ansari, and J. C. Yao, “Some iterative methods for finding fixed points and for solving constrained convex minimization problems,” Nonlinear Analysis, vol. 74, no. 16, pp. 5286–5302, 2011.
- H. Iiduka, “Iterative algorithm for solving triple-hierarchical constrained optimization problem,” Journal of Optimization Theory and Applications, vol. 148, no. 3, pp. 580–592, 2011.
- G. Marino and H. K. Xu, “Explicit hierarchical fixed point approach to variational inequalities,” Journal of Optimization Theory and Applications, vol. 149, no. 1, pp. 61–78, 2011.
- Y. H. Wang and W. Xu, “Strong covergence of a modified iterative algorithm for hierarchical fixed point problems and variational inequalities,” Fixed Point Theory and Applications, vol. 2013, article 121, 2013.
- H. K. Xu, “Viscosity method for hierarchical fixed point approach to variational inequalities,” Taiwanese Journal of Mathematics, vol. 14, no. 2, pp. 463–478, 2010.
- Y. Yao, Y. J. Cho, and Y. C. Liou, “Iterative algorithms for hierarchical fixed points problems and variational inequalities,” Mathematical and Computer Modelling, vol. 52, no. 9-10, pp. 1697–1705, 2010.
- M. Tian, “A general iterative algorithm for nonexpansive mappings in Hilbert spaces,” Nonlinear Analysis, vol. 73, no. 3, pp. 689–694, 2010.
- I. Yamada, “The hybrid steepest-descent method for variational inequality problems over the intersection of the fixed-point sets of nonexpansive mappings,” Studies in Computational Mathematics, vol. 8, pp. 473–504, 2001.
- M. Tian and L. Y. Di, “Synchronal algorithm and cyclic algorithm for fixed point problems and variational inequality problems in Hilbert spaces,” Fixed Point Theory and Applications, vol. 2011, article 21, 2011.
- S. N. He and W. W. Sun, “New hybrid steepest descent algorithms for variational inequalities over the common fixed points set of infinite nonexpansive mappings,” WSEAS Transactions on Mathematics, vol. 11, no. 2, pp. 83–92, 2012.