- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Journal of Applied Mathematics
Volume 2013 (2013), Article ID 986317, 6 pages
A Conjugate Gradient Type Method for the Nonnegative Constraints Optimization Problems
College of Mathematics, Honghe University, Mengzi 661199, China
Received 16 December 2012; Accepted 20 March 2013
Academic Editor: Theodore E. Simos
Copyright © 2013 Can Li. 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.
- M. R. Hestenes and E. Stiefel, “Methods of conjugate gradients for solving linear systems,” Journal of Research of the National Bureau of Standards, vol. 49, pp. 409–436, 1952.
- R. Fletcher and C. M. Reeves, “Function minimization by conjugate gradients,” The Computer Journal, vol. 7, pp. 149–154, 1964.
- B. Polak and G. Ribire, “Note sur la convergence de directions conjugees,” Revue Française d'Informatique et de Recherche Opérationnelle, 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, Practical Methods of Optimization, John Wiley & Sons Ltd., Chichester, UK, 2nd edition, 1987.
- Y. Liu and C. Storey, “Efficient generalized conjugate gradient algorithms. I. Theory,” Journal of Optimization Theory and Applications, vol. 69, no. 1, pp. 129–137, 1991.
- 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.
- M. J. D. Powell, “Convergence properties of algorithms for nonlinear optimization,” SIAM Review, vol. 28, no. 4, pp. 487–500, 1986.
- J. C. Gilbert and J. Nocedal, “Global convergence properties of conjugate gradient methods for optimization,” SIAM Journal on Optimization, vol. 2, no. 1, pp. 21–42, 1992.
- R. Pytlak, “On the convergence of conjugate gradient algorithms,” IMA Journal of Numerical Analysis, vol. 14, no. 3, pp. 443–460, 1994.
- G. Li, C. Tang, and Z. Wei, “New conjugacy condition and related new conjugate gradient methods for unconstrained optimization,” Journal of Computational and Applied Mathematics, vol. 202, no. 2, pp. 523–539, 2007.
- X. Li and X. Zhao, “A hybrid conjugate gradient method for optimization problems,” Natural Science, vol. 3, no. 1, pp. 85–90, 2011.
- Y. H. Dai and Y. Yuan, “An efficient hybrid conjugate gradient method for unconstrained optimization,” Annals of Operations Research, vol. 103, pp. 33–47, 2001.
- W. W. Hager and H. Zhang, “A new conjugate gradient method with guaranteed descent and an efficient line search,” SIAM Journal on Optimization, vol. 16, no. 1, pp. 170–192, 2005.
- D.-H. Li, Y.-Y. Nie, J.-P. Zeng, and Q.-N. Li, “Conjugate gradient method for the linear complementarity problem with -matrix,” Mathematical and Computer Modelling, vol. 48, no. 5-6, pp. 918–928, 2008.
- D.-H. Li and X.-L. Wang, “A modified Fletcher-Reeves-type derivative-free method for symmetric nonlinear equations,” Numerical Algebra, Control and Optimization, vol. 1, no. 1, pp. 71–82, 2011.
- L. Zhang, W. Zhou, and D. Li, “Global convergence of a modified Fletcher-Reeves conjugate gradient method with Armijo-type line search,” Numerische Mathematik, vol. 104, no. 4, pp. 561–572, 2006.
- 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.
- D. H. Li and X. J. Tong, Numerical Optimization, Science Press, Beijing, China, 2005.
- J. J. Moré, B. S. Garbow, and K. E. Hillstrom, “Testing unconstrained optimization software,” ACM Transactions on Mathematical Software, vol. 7, no. 1, pp. 17–41, 1981.