A scaled BFGS preconditioned conjugate gradient algorithm for unconstrained optimization

Applied Mathematics Letters

Volumn 20, Issue 6, 2007, Pages 645-650

  Andrei, Neculai ^a  

^a NATIONAL INSTITUTE FOR RESEARCH AND DEVELOPMENT IN INFORMATICS   (Romania)

Author keywords

BFGS preconditioning; Conjugate gradient method; Unconstrained optimization

Indexed keywords

ALGORITHMS; CONJUGATE GRADIENT METHOD; CONSTRAINT THEORY; MATRIX ALGEBRA; NONLINEAR PROGRAMMING; PROBLEM SOLVING;

COMPUTATIONAL RESULTS; SPECTRAL CONJUGATE GRADIENTS; SPECTRAL GRADIENT; UNCONSTRAINED OPTIMIZATION PROBLEMS;

OPTIMIZATION;

EID: 33947268766     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aml.2006.06.015     Document Type: Article

References (14)

1. Birgin E., and Martínez J.M. A spectral conjugate gradient method for unconstrained optimization. Appl. Math. Optim. 43 (2001) 117-128
2. Bongartz I., Conn A.R., Gould N.I.M., and Toint P.L. CUTE: Constrained and unconstrained testing environments. ACM Trans. Math. Software 21 (1995) 123-160
3. Dai Y.H., and Liao L.Z. New conjugate conditions and related nonlinear conjugate gradient methods. Appl. Math. Optim. 43 (2001) 87-101
4. Fletcher R., and Reeves C.M. Function minimization by conjugate gradients. Comput. J. 7 (1964) 149-154
5. Hestenes M.R., and Stiefel E. Methods of conjugate gradients for solving linear systems. J. Res. Nat. Bur. Stan. Sec. B 48 (1952) 409-436
6. Liu D., and Nocedal J. On the limited memory BFGS method for large scale optimization. Math. Program. B 45 (1989) 503-528
7. Nocedal J. http://www.ece.northwestern.edu/~nocedal/lbfgs.html
8. J.M. Perry, A class of conjugate gradient algorithms with a two step variable metric memory, Discussion paper 269, Center for Mathematical Studies in Economics and Management Science, Northwestern University, 1977
9. Polak E., and Ribière G. Note sur la convergence de méthodes de directions conjuguées. Revue Francaise Informat. Reserche Opérationnelle, 3e Année 16 (1969) 35-43
10. Powell M.J.D. Restart procedures for the conjugate gradient method. Math. Program. 12 (1977) 241-254
11. Shanno D.F. Conjugate gradient methods with inexact searches. Math. Oper. Res. 3 (1978) 244-256
12. Shanno D.F. On the convergence of a new conjugate gradient algorithm. SIAM J. Numer. Anal. 15 (1978) 1247-1257
13. Wolfe P. Convergence conditions for ascent methods. SIAM Rev. 11 (1969) 226-235
14. Wolfe P. Convergence conditions for ascent methods II: Some corrections. SIAM Rev. 13 (1971) 185-188