New properties of a nonlinear conjugate gradient method

Numerische Mathematik

Volumn 89, Issue 1, 2001, Pages 83-98

  Dai, Yu Hong ^a  

^a INSTITUTE OF COMPUTATIONAL MATHEMATICS AND SCIENTIFIC ENGINEERING COMPUTING   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035614397     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00005464     Document Type: Article

References (21)

1. L. Armijo, Minimization of functions having Lipschitz continuous first partial derivatives. Paci. J. Math. 16(1), 1-3 (1966)
2. A. Buckley, Conjugate gradient methods, in: M. J. D. Powell, ed., Nonlinear Optimization 1981, pp. 17-22, London: Academic Press (1982)
3. R. H. Byrd, J. Nocedal, A Tool for the Analysis of Quasi-Newton Methods with Application To Unconstrained Minimization. SIAM J. Numer. Anal. 26(3), 727-739 (1989)
4. Y. H. Dai, Analyses of Nonlinear Conjugate Gradient Methods, Ph.D. thesis, Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, 1997
5. Y. H. Dai, Y. Yuan, A Nonlinear Conjugate Gradient Method with A Strong Global Convergence Property. SIAM Journal on Optimization 10(1), 177-182 (1999)
6. Y. H. Dai, Y. Yuan, Some properties of a new conjugate gradient method, in: Y. Yuan ed., Advances in Nonlinear Programming pp. 251-262, Boston: Kluwer 1998
7. J. W. Daniel, The conjugate gradient method for linear and nonlinear operator equations. SIAM J. Numer. Anal. 4, 10-26 (1967)
8. R. Fletcher, Practical Methods of Optimization vol. 1: Unconstrained Optimization. New York: John Wiley & Sons (1987)
9. R. Fletcher, C. Reeves, Function minimization by conjugate gradients, Comput. J. 7, 149-154 (1964)
10. J. C. Gilbert, J. Nocedal, Global convergence properties of conjugate gradient methods for optimization. SIAM J. Opt. 2(1), 21-42 (1992)
11. L. Grippo, F. Lampariello, S. Lucidi, Global convergence and stabilization of unconstrained minimization methods without derivatives. J Opt. Theory Appli. 56, 385-406 (1988)
12. M. R. Hestenes, E. L. Stiefel, Methods of conjugate gradients for solving linear systems. J. Res. Nat. Bur. Standards Sect. 5(49), 409-436 (1952)
13. R. De Leone, M. Gaudioso, L. Grippo, Stopping criteria for linesearch methods without derivatives. Mathematical Programming 30, 285-300 (1984)
14. J. J. Morè, B. S. Garbow, K. E. Hillstrom, Testing unconstrained optimization software. ACM Transact. on Math. Software 7, 17-41 (1981)
15. Y. Liu, C. Storey, Efficient Generalized Conjugate Gradient Algorithms, Part 1: Theory. J. Opt. Theory Appli. 69, 129-137 (1991)
16. J. L. Nazareth, Conjugate-gradient Methods, to appear in: C. Floudas, P. Pardalos, eds., Encyclopedia of Optimization (Kluwer Academic Publishers, Boston, USA and Dordrecht, The Netherlands 1999)
17. M. J. D. Powell, Restart procedures of the conjugate gradient method. Math. Program. 2, 241-254 (1977)
18. E. Polak, G. Ribière, Note sur la convergence de directions conjugées. Rev. Francaise Informat Recherche Opertionelle, 3e Année 16, 35-43 (1969)
19. B. T. Polyak, The conjugate gradient method in extremem problems, USSR Comp. Math. Math. Phys. 9, 94-112 (1969)
20. D. F. Shanno, Conjugate gradient methods with inexact searches, Math. Oper. Res. 3, 244-256 (1978)
21. G. Zoutendijk, Nonlinear Programming, Computational Methods, in: Integer and Nonlinear Programming (J. Abadie, ed.), North-Holland (Amsterdam), pp. 37-86, 1970