A modified CG-DESCENT method for unconstrained optimization

Journal of Computational and Applied Mathematics

Volumn 235, Issue 11, 2011, Pages 3332-3341

  Dai, Zhifeng ^a   Wen, Fenghua ^a  

^a CHANGSHA UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

Conjugate gradient method; Global convergence; Sufficient descent property; Unconstrained optimization

Indexed keywords

DESCENT METHOD; GENERAL METHOD; GLOBAL CONVERGENCE; GLOBALLY CONVERGENT; LINE SEARCHES; NUMERICAL RESULTS; SUFFICIENT CONDITIONS; SUFFICIENT DESCENT PROPERTY; UNCONSTRAINED OPTIMIZATION;

NUMERICAL METHODS; OPTIMIZATION;

CONJUGATE GRADIENT METHOD;

EID: 79953236946     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2011.01.046     Document Type: Article

References (19)

1. M.R. Hestenes, and E.L. Stiefel Methods of conjugate gradients for solving linear systems J. Res. Natl. Bur. Stand. Sec. B 49 1952 409 432
2. B. Polak, and G. Ribire Note surla convergence des mthodes de directions conjugues Rev. Fr. Autom. Inform. Rech. Oper.,3e Anne. 16 1969 35 43
3. B.T. Polyak The conjugate gradient method in extreme problems USSR Comput. Math. Math. Phys. 9 1969 94 112
4. Y.L. Liu, and C.S. Storey Efficient generalized conjugate gradient algorithms, part 1: theory J. Optim. Theory Appl. 69 1991 129 137
5. Y.H. Dai, and Y. Yuan A nonlinear conjugate gradient method with a strong global convergence property SIAM J. Optim. 10 2000 177 182
6. R. Fletcher, and C. Reeves Function minimization by conjugate gradients Comput. J. 7 1964 149 154
7. R. Fletcher Practical Methods of Optimization, Vol I: Unconstrained Optimization 1987 Wiley & Sons New York
8. M. Al-Baali Descent property and global convergence of the FletcherCReeves method with inexact line search IMA J. Numer. Anal. 5 1985 121 124
9. G. Liu, J. Han, and H. Yin Global convergence of the FletcherReeves algorithm with inexact line search Appl. Math. J. Chinese Univ. Ser. B 10 1995 75 82
10. J.C. Gilbert, and J. Nocedal Global convergence properties of conjugate gradient methods for optimization SIAM J. Optim. 2 1992 21 42
11. W.W. Hager, and H. Zhang A new conjugate gradient method with guaranteed descent and an efficient line search SIAM J. Optim. 16 2005 170 192
12. W.Y. Cheng A two-term PRP-based descent method Numer. Funct. Anal. Optim. 28 2007 1217 1230
13. L. Zhang, W.J. Zhou, and D.H. Li Global convergence of a modified FletcherReeves conjugate method with Armijo-type line search Numer. Math. 104 2006 561 572 (Pubitemid 44483263)
14. G. Zoutendijk J. Abadie, Nonlinear Programming, Computational Methods Integer and Nonlinear Programming 1970 North-Holland Amsterdam 37 86
15. P. Wolfe Convergence conditions for ascent methods SIAM Rev. 11 1969 226 235
16. Y.H. Dai, and L.Z. Liao New conjugacy conditions and related nonlinear conjugate gradient methods Appl. Math. Optim. 43 2001 87 101
17. K.E. Bongartz, A.R. Conn, N.I.M. Gould, and P.L. Toint CUTE: constrained and unconstrained testing environments ACM Trans. Math. Software 21 1995 123 160
18. L. Zhang, W.J. Zhou, and D.H. Li A descent modified PolakRibirePolyak conjugate gradient method and its global convergence IMA J. Numer. Anal. 26 2006 629 640 (Pubitemid 44546419)
19. E.D. Dolan, and J.J. Mor Benchmarking optimization software with performance profiles Math. Program. 91 2002 201 213 (Pubitemid 44744777)