Spectral conjugate gradient methods with sufficient descent property for large-scale unconstrained optimization

Optimization Methods and Software

Volumn 23, Issue 2, 2008, Pages 275-293

  Yu, Gaohang ^a   Guan, Lutai ^a   Chen, Wufan ^b  

^a SUN YAT SEN UNIVERSITY   (China)

^b SOUTHERN MEDICAL UNIVERSITY   (China)

Author keywords

Global convergence; Large scale optimization; Spectral conjugate gradient method; Unconstrained optimization

Indexed keywords

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; GRADIENT METHODS; LARGE SCALE SYSTEMS; PROBLEM SOLVING;

GLOBAL CONVERGENCE; LARGE-SCALE OPTIMIZATION; UNCONSTRAINED OPTIMIZATION;

CONSTRAINED OPTIMIZATION;

EID: 40249089958     PISSN: 10556788     EISSN: 10294937     Source Type: Journal    
DOI: 10.1080/10556780701661344     Document Type: Article

References (26)

1. N. Andrei, Scaled memoryless BFGS preconditioned conjugate gradient algorithm for unconstrained optimization, Optim. Methods Softw. 22(4) (2007), 561-571.
2. J. Barzilai and J.M. Borwein, Two point step size gradient methods, IMA J. Numer. Anal. 8 (1988), 141-148.
3. E.G. Birgin and J.M. Martinez, A spectral conjugate gradient method for unconstrained optimization, Appl. Math. Optim. 43 (200.1), 117-128.
4. I. Bongartz et al., CUTE: constrained and unconstrained testing environments, ACM Trans. Math. Softw. 21 (1995), 123-160.
5. Y.H. Dai and L.Z. Liao, New conjugacy conditions and related nonlinear conjugate gradient methods, Appl. Math. Optim. 43 (200.1), 87-101.
6. Y.H. Dai and Y.X. Yuan, A nonlinear conjugate gradient with a strong global convergence properties, SIAM J. Optim. 10 (2000), 177-182.
7. E.D. Dolan and J. Moré, Benchmarking optimization software with performance profiles, Math. Program. Ser. A. 91 (2002), 201-213.
8. R. Fletcher, Practical Method of Optimization, Volume, 1: Unconstrained Optimization, 2nd ed., Wiley, New York, 1997.
9. R. Fletcher and C.M. Reeves, Function minimization by conjugate gradients, Comput. J. 7 (1964), 149-154.
10. J.C. Gibert 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.W. Hager and H. Zhang, CG_DESCENT: A conjugate gradient method with guaranteed descent, ACM Trans. Math. Softw. 32 (2006), 113-137.
13. W.W. Hager and H. Zhang, A survey of nonlinear conjugate gradient methods, Pac. J. Optim. 2 (2006), 35-58.
14. M.R. Hestenes and E. Stiefel, Method of conjugate gradient for solving linear equations, J. Res. Nat. Bur. Stand. 49 (1952), 409-436.
15. Y. Liu and C. Storey, Efficient generalized conjugate gradient algorithms, part I: theory, J. Optim. Theory Appl. 69 (1991), 129-137.
16. A. Perry, A modified conjugate gradient algorithm, Oper. Res. 26 (1978), 1073-1078.
17. E. Polak and G. Ribiére, Note Sur la convergence de directions conjugèes, Rev. Francaise Informat Recherche Operationelle, 3e Annèe. 16 (1969), 35-43.
18. B.T. Polyak, The conjugate gradient method in extreme problems, USSR Comp. Math. Math. Phys. 9 (1969), 94-112.
19. M.J.D. Powell, Nonconvex minimization calculations and the conjugate gradient method, Lecture Notes in Mathematics, Vol 1. 1066, Springer-Verlag, Berlin, 1984, 122-141.
20. Z.X. Wei, G. Y. Li and L. Q. Qi, New nonlinear conjugate gradient formulas for large-scale unconstrained optimization problems, Appl. Math. Comput. 179 (2006), 407-430.
21. G.H. Yu, Y.L. Zhao and Z.X. Wei, A descent nonlinear conjugate gradient method for large-scale unconstrained optimization, Appl. Math. Comput. 187 (2007), 636-643.
22. G.H. Yu and L.T. Guan, New descent nonlinear conjugate gradient methods for large-scale unconstrained optimization, Tech. Rep. Department of Scientific Computation and Computer Applications, Sun Yat-Sen University, Guangzhou, P.R. China, 2005.
23. P.Wolfe, Convergence conditions for ascent methods, SIAM Rev. 11 (1969), 226-235.
24. L. Zhang, W. Zhou and D. Li, Global convergence of a modified Fletcher-Reeves conjugate gradient method with Armijo-type line search, Numerische Mathematik. 104 (2006), 561-572.
25. L. Zhang, W. Zhou and D. Li, A descent modified Polak-Ribiere-Polyak conjugate gradient method and its global convergence, IMA J. Numer. Anal. 26 (2006), 629-640.
26. G. Zoutendijk, Nonlinear programming computational methods, in Integer and Nonlinear Programming, J. Abadie, ed., North-Holland, Amsterdam. 1970, pp. 37-86.