Some descent three-term conjugate gradient methods and their global convergence

Optimization Methods and Software

Volumn 22, Issue 4, 2007, Pages 697-711

  Zhang, Li ^a   Zhou, Weijun ^b   Li, Donghui ^b  

^a CHANGSHA UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^b HUNAN UNIVERSITY   (China)

Author keywords

Global convergence; Three term conjugate gradient method

Indexed keywords

FUNCTION EVALUATION; GLOBAL OPTIMIZATION;

GLOBAL CONVERGENCE; THREE TERM CONJUGATE GRADIENT METHOD;

CONVERGENCE OF NUMERICAL METHODS;

EID: 34147202932     PISSN: 10556788     EISSN: 10294937     Source Type: Journal    
DOI: 10.1080/10556780701223293     Document Type: Article

References (29)

1. Fletcher, R. and Reeves, C., 1964, Function minimization by conjugate gradients. Computer Journal, 7, 149-154.
2. Polak, B. and Ribiere, G., 1969, Note surla convergence des méthodes de directions conjuguées. Revue Francaise de Recherche Operationnele, 16, 35-43.
3. Polyak, B.T., 1969, The conjugate gradient method in extreme problems. USSR Computational Mathematics and Mathematical Physics, 9, 94-112.
4. Hestenes, M.R. and Stiefel, E.L., 1952, Method of conjugate gradient for solving linear systems. Journal of Reseench of the National Bureau of Standards, 49, 409-432.
5. Dai, Y.H. andYuan, Y., 2000, A nonlinear conjugate gradient method with a strong global convergence property. SIAM Journal on Optimization, 10, 177-182.
6. Fletcher, R., 1987, Practical Methods of Optimization, Vol. 1: Unconstrained Optimization (New York: Wiley & Sons).
7. Zoutendijk, G., 1970, Nonlinear Programming, Computational methods. In: J. Abadie (Ed.) Integer and Nonlinear Programming (Amsterdam: North-Holland), pp. 37-86.
8. Al-Baali, M., 1985, Descent property and global convergence of the Fletcher-Reeves method with inexact line search. IMA Journal of Numerical Analysis, 5, 121-124.
9. Liu, G., Han, J. and Yin, H., 1995, Global convergence of the Fletcher-Reeves algorithm with inexact line search. Applied Mathematical Journal of Chinese Universities Serial B, 10, 75-82.
10. Dai, Y.H. andYuan, Y., 1996, Convergence properties of the Fletcher-Reeves method. IMA Journal of Numerical Analysis, 16, 155-164.
11. Gilbert, J.C. and Nocedal, J., 1992, Global convergence properties of conjugate gradient methods for optimization. SIAM Journal on Optimization, 2, 21-42.
12. Grippo, L. and Lucidi, S., 1997, A globally convergent version of the Polak-Ribiére gradient method. Mathematical Programming, 78, 375-391.
13. Hager, W.W. and Zhang, H., 2005, A new conjugate gradient method with guaranteed descent and an efficient line search. SIAM Journal on Optimization, 16, 170-192.
14. Dai, Y.H. and Yuan, Y., 2000, Nonlinear Conjugate Gradient Methods (Shanghai: Shanghai Science and Technology Publisher).
15. Hager, W.W. and Zhang, H., 2006, A survey of nonlinear conjugate gradient methods. Pacific Journal of Optimization, 2, 35-58.
16. Beale, E.M.L., 1972, A derivation of conjugate gradients. In: F.A. Lootsma (Ed.) Numerical Methods for Nonlinear Optimization (New York: Academic Press), pp. 39-43.
17. Nazareth, J.L., 1977, Conjugate direction algorithm without line searchs. Journal of Optimization Theory and Applications, 23, 373-387.
18. Nocedal, J., 1980, Updating quasi-Newton matrixes with limited storage. Mathematics of Computation, 35, 773-782.
19. Shanno, D.F., 1978, Conjugate gradient methods with inexact searches. Mathematics of Operations Research, 3, 244-256.
20. Zhang, L., Zhou, W. and Li, D., 2006, A descent modified Polak-Ribière-Polyak conjugate gradient method and its global convergence. IMA Journal of Numerical Analysis, 26, 629-640.
21. Zhang, L., Zhou, W. and Li, D., 2006, Global convergence of a modified Fletcher-Reeves conjugate gradient method with Armijo-type line search. Numerische Mathematik, 104, 561-572.
22. Li, D.H. and Fukushima, M., 2001, A modified BFGS method and its global convergence in nonconvex minimization. Journal of Computational and Applied Mathematics, 129, 15-35.
23. Li, D.H. and Fukushima, M., 2001, On the global convergence of the BFGS method for nonconvex unconstrained optimization problems. SIAM Journal on Optimization, 11, 1054-1064.
24. Zhou, W. and Zhang, L., 2006, A nonlinear conjugate gradient method based on the MBFGS secant condition. Optimization Methods and Software, 21, 707-714.
25. Wolfe, P., 1969, Convergence conditions for ascent methods. SIAM Review, 11, 226-235.
26. Bongartz, K.E., Conn, A.R., Gould, N.I.M. and Toint, P.L., 1995, CUTE: constrained and unconstrained testing environments. ACM Transactions of Mathematical Software, 21, 123-160.
27. Liu, D.C. and Nocedal, J., 1989, On the limited memory BFGS method for large scale optimization methods. Mathematical Programming, 45, 503-528.
28. Dolan, E.D. and Moré, J.J., 2002, Benchmarking optimization software with performance profiles. Mathematical Programming, 91, 201-213.
29. Moré, J.J. and Thuente, D.J., 1994, Line search algorithms with guaranteed sufficient decrease. ACM Transactions of Mathematical Software, 20, 286-307.