- 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 2014 (2014), Article ID 283215, 7 pages
On the Strong Convergence of a Sufficient Descent Polak-Ribière-Polyak Conjugate Gradient Method
1School of Mathematics and Statistics, Zaozhuang University, Shandong 277160, China
2School of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou 310018, China
Received 2 December 2013; Revised 9 January 2014; Accepted 10 January 2014; Published 23 February 2014
Academic Editor: Sergei V. Pereverzyev
Copyright © 2014 Min Sun and Jing Liu. 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.
- B. Polak and G. Ribière, “Note surla convergence des méthodes de directions conjuguées,” Revue Francaise Imformat Recherche Opertionelle, vol. 16, pp. 35–43, 1969.
- B. T. Polyak, “The conjugate gradient method in extremal problems,” USSR Computational Mathematics and Mathematical Physics, vol. 9, no. 4, pp. 94–112, 1969.
- R. Fletcher and C. Reeves, “Function minimization by conjugate gradients,” The Computer Journal, vol. 7, pp. 149–154, 1964.
- M. R. Hestenes and E. L. Stiefel, “Method of conjugate gradient for solving linear systems,” Journal of Research of the National Bureau of Standards, vol. 49, pp. 409–432, 1952.
- L. Zhang, W. J. Zhou, and D. H. Li, “Some descent three-term conjugate gradient methods and their global convergence,” Optimization Methods and Software, vol. 22, no. 4, pp. 697–711, 2007.
- Y. H. Dai and Y. Yuan, “A nonlinear conjugate gradient method with a strong global convergence property,” SIAM Journal on Optimization, vol. 10, no. 1, pp. 177–182, 1999.
- L. Zhang, W. Zhou, and D. H. Li, “A descent modified Polak-Ribière-Polyak conjugate gradient method and its global convergence,” IMA Journal of Numerical Analysis, vol. 26, no. 4, pp. 629–640, 2006.
- Z. J. Shi and J. Shen, “Convergence of the Polak-Ribière-Polyak conjugate gradient method,” Nonlinear Analysis, Theory, Methods and Applications, vol. 66, no. 6, pp. 1428–1441, 2007.
- Z.-J. Shi and J. Shen, “Convergence of Liu-Storey conjugate gradient method,” European Journal of Operational Research, vol. 182, no. 2, pp. 552–560, 2007.
- W. J. Zhou and Y. H. Zhou, “On the strong convergence of a modified Hestenes-Stiefel method for nonconvex optimization,” Journal of Industrial and Management Optimization, vol. 9, no. 4, pp. 893–899, 2013.
- A. Neculai, http://camo.ici.ro/neculai/UNO/UNO.FOR.
- E. D. Dolan and J. J. Moré, “Benchmarking optimization software with performance profiles,” Mathematical Programming B, vol. 91, no. 2, pp. 201–213, 2002.