Two fundamental convergence theorems for nonlinear conjugate gradient methods and their applications

Acta Mathematicae Applicatae Sinica

Volumn 17, Issue 1, 2001, Pages 38-46

  Han, Jiye ^a   Liu, Guanghui ^b   Sun, Defeng ^c   Yin, Hongxia ^a  

^a INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

^b Northwestern University   (United States)

^c University of New Sourth Wales   (Australia)

Author keywords

Conjugate gradient method; Descent condition; Global convergence

Indexed keywords

EID: 33144464011     PISSN: 01689673     EISSN: 16183932     Source Type: Journal    
DOI: 10.1007/bf02669682     Document Type: Article

References (12)

1. R. Fletcher, C.M. Reeves. Function Minimization by Conjugate Gradients. Comput. J., 1964, 7: 149-154
2. G. Zoutendijk. Nonlinear Programming, Computational Methods. In: Integer and Nonlinear Programming, J. Abadie, ed., North-Holland, Amsterdam, 1970, 37-86
3. M. Al-Baali. Descent Property and Global Convergence of the Fletcher-Reeves Method with Inexact Linesearch. IMA J. Numer. Anal., 1985, 5: 121-124
4. E. Polak, G. Ribière. Note sur la Convergence de Méthods de Directions Conjugées. Revue Francaise d'Informatique et de Recherche Opiérationnelle, 1969, 16: 35-43
5. M. R. Hestenes, E. Stiefel. Method of Conjugate Gradient for Solving Linear System. J. Res. Nat. Bur. Stand., 1952, 49: 409-436
6. M.J.D. Powell. Nonconvex Minimization Calculations and the Conjugate Gradient Method. In Lecture Notes in Mathematics 1066, Springer-Verlag, Berlin, 1984, 122-141
7. D. Touati-Ahmed, C. Storey. Global Convergent Hybrid Conjugate Gradient Methods. J. Optim. Theory Appl., 1990, 64: 379-397
8. Y.F. Hu, C. Storey. Global Convergence Result for Conjugate Gradient Methods. J. Optim. Theory Appl., 1991, 71: 399-405
9. J.C. Gilbert, J. Nocedal. Global Convergence Properties of Conjugate Gradient Methods for Optimization. SIAM J. Optimization, 1992, 2: 21-42
10. P. Wolfe. Convergence Conditions for Ascent Methods. SIAM Rev., 1969, 11: 226-235
11. J.J. More, D.J. Thuente. On Line Search Algorithms with Guaranteed Decrease. ACM Trans. Math. Software, 1994, 20: 286-307
12. J.B. Hiriart-Urruty, C. Lemaréchal. Convex Analysis and Minimization Algorithms, Vols. 1 and 2. Springer-Verlag, Berlin, Heidelberg, New York, 1993