New conjugacy condition and related new conjugate gradient methods for unconstrained optimization

Journal of Computational and Applied Mathematics

Volumn 202, Issue 2, 2007, Pages 523-539

  Li, Guoyin ^a   Tang, Chunming ^a,b   Wei, Zengxin ^a  

^a GUANGXI UNIVERSITY   (China)

^b SHANGHAI UNIVERSITY   (China)

Author keywords

Conjugacy condition; Conjugate gradient method; Global convergence; Quasi Newton equation; Unconstrained optimization

Indexed keywords

CONSTRAINT THEORY; CONVERGENCE OF NUMERICAL METHODS; FUNCTION EVALUATION; GRADIENT METHODS; NONLINEAR CONTROL SYSTEMS; NUMERICAL METHODS;

CONJUGACY CONDITION; CONJUGATE GRADIENT METHOD; GLOBAL CONVERGENCE; QUASI NEWTON EQUATION; UNCONSTRAINED OPTIMIZATION;

OPTIMIZATION;

EID: 33847062894     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2006.03.005     Document Type: Article

References (21)

1. Al-Baali A. Descent property and global convergence of the Fletcher-Reeves method with inexact line search. IMA J. Numer. Anal. 5 (1985) 121-124
2. Armijo L. Minimization of functions having Lipschitz conditions partial derivatives. Pacific J. Math. 16 (1966) 1-3
3. X. Chen, J. Sun, Global convergence of two-parameter family of conjugate gradient methods without line search, J. Comput. Appl. Math. 146 (2002) 37-45.
4. Y. Dai, Convergence of Polak-Ribière-Polyak conjugate gradient method with constant stepsizes, Manuscript, Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, 2001.
5. Dai Y., Han J., Liu G., Sun D., Yin H., and Yan Y. Convergence properties of nonlinear conjugate methods. SIAM J. Optim. 2 (1999) 345-358
6. Dai Y., and Liao L.Z. New conjugacy conditions and related nonlinear conjugate gradient methods. Appl. Math. Optim. 43 (2001) 87-101
7. Y. Dai, Y. Yuan, Further studies on the Polak-Ribière-Polyak method, Research Report ICM-95-040, Institute of Computational Mathematics and Scientific/ Engineering Computing, Chinese Academy of Sciences, 1995.
8. Dai Y., and Yuan Y. Nonlinear Conjugate Gradient Methods (2000), Science Press of Shanghai, Shanghai
9. Gibert J.C., and Nocedal J. Global convergence properties of conjugate gradient methods for optimization. SIAM J. Optim. 2 (1992) 21-42
10. Moreau J.J. Proximite et dualite dans un espace hilbertien. Bull. Soc. Math. France 93 (1965) 273-299
11. Morè J.J., Garbow B.S., and Hillstrome K.E. Testing unconstrained optimization software. AVM Trans. Math. Software 7 (1981) 17-41
12. Nocedal J. Conjugate gradient methods and nonlinear optimization. In: Adams L., and Nazareth J.L. (Eds). Linear and Nonlinear Conjugate Gradient Related Methods (1995), SIAM, Philadelphia, PA 9-23
13. Powell M.J.D. Restart procedures for the conjugate gradient method. Math. Programming 12 (1977) 241-254
14. M.J.D. Powell, Nonconvex Minimization Calculations and the Conjugate Gradient Method, in: Lecture Notes in Mathematics, vol. 1066, Springer, Berlin, 1984, pp. 122-141.
15. Z. Wei, G. Li, L. Qi, New quasi-newton methods for unconstrain optimization, preprint.
16. Wei Z., and Qi L. Convergence analysis of a proximal Newton method. Numer. Funct. Anal. Optim. 17 (1996) 463-472
17. Wei Z., Qi L., and Birge J.R. A new method for nonsmooth convex optimization. J. Inequalities Appl. 2 (1998) 157-179
18. Wei Z., Yu G., Yuan G., and Lian Z. The superlinear convergence of a modified BFGS-type method for unconstrained optimization. Comput. Optim. Appl. 29 3 (2004) 315-332
19. Wolfe P. Convergence conditions for ascent methods. SIAM Rev. 11 (1969) 226-235
20. Wolfe P. Convergence conditions for ascent methods II: some corrections. SIAM Rev. 11 (1971) 185-188
21. Zoutendijk G. Nonlinear programming computational methods. In: Jabadie (Ed). Integer and Nonlinear Programming (1970), North-Holland, Amsterdam 37-86