- 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
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 742815, 5 pages
Nonlinear Conjugate Gradient Methods with Wolfe Type Line Search
College of Mathematics, Qingdao University, Qingdao 266071, China
Received 20 January 2013; Accepted 6 February 2013
Academic Editor: Yisheng Song
Copyright © 2013 Yuan-Yuan Chen and Shou-Qiang Du. 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. 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. M. Reeves, “Function minimization by conjugate gradients,” The Computer Journal, vol. 7, pp. 149–154, 1964.
- M. R. Hestenes, “E.Stiefel. Method of conjugate gradient for solving linear equations,” Journal of Research of the National Bureau of Standards, vol. 49, pp. 409–436, 1952.
- 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.
- R. Fletcher, Practical Methods of Optimization, Unconstrained Optimization, Wiley, New York, NY, USA, 2nd edition, 1987.
- M. Raydan, “The Barzilai and Borwein gradient method for the large scale unconstrained minimization problem,” SIAM Journal on Optimization, vol. 7, no. 1, pp. 26–33, 1997.
- L. Zhang and W. Zhou, “Two descent hybrid conjugate gradient methods for optimization,” Journal of Computational and Applied Mathematics, vol. 216, no. 1, pp. 251–264, 2008.
- A. Zhou, Z. Zhu, H. Fan, and Q. Qing, “Three new hybrid conjugate gradient methods for optimization,” Applied Mathematics, vol. 2, no. 3, pp. 303–308, 2011.
- B. C. Jiao, L. P. Chen, and C. Y. Pan, “Global convergence of a hybrid conjugate gradient method with Goldstein line search,” Mathematica Numerica Sinica, vol. 29, no. 2, pp. 137–146, 2007.
- G. Yuan, “Modified nonlinear conjugate gradient methods with sufficient descent property for large-scale optimization problems,” Optimization Letters, vol. 3, no. 1, pp. 11–21, 2009.
- Z. Dai and B. Tian, “Global convergence of some modified PRP nonlinear conjugate gradient methods,” Optimization Letters, vol. 5, no. 4, pp. 615–630, 2011.
- C. Y. Wang, Y. Y. Chen, and S. Q. Du, “Further insight into the Shamanskii modification of Newton method,” Applied Mathematics and Computation, vol. 180, no. 1, pp. 46–52, 2006.
- 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.
- L. Grippo, F. Lampariello, and S. Lucidi, “A nonmonotone line search technique for Newton's method,” SIAM Journal on Numerical Analysis, vol. 23, no. 4, pp. 707–716, 1986.