Wide interval for efficient self-scaling quasi-Newton algorithms

Optimization Methods and Software

Volumn 20, Issue 6, 2005, Pages 679-691

  Al Baali, Mehiddin ^a   Khalfan, Humaid ^b  

^a SULTAN QABOOS UNIVERSITY   (Oman)

^b UNITED ARAB EMIRATES UNIVERSITY   (United Arab Emirates)

Author keywords

Broyden's family; Global and superlinear convergence; Quasi Newton methods; Self scaling; Unconstrained optimization

Indexed keywords

COMPUTATIONAL METHODS; CONVERGENCE OF NUMERICAL METHODS; OPTIMIZATION; PERFORMANCE;

BROYDEN'S FAMILY; GLOBAL AND SUPERLINEAR CONVERGENCE; QUASI-NEWTON METHODS; SELF-SCALING; UNCONSTRAINED OPTIMIZATION;

ALGORITHMS;

EID: 29744452629     PISSN: 10556788     EISSN: 10294937     Source Type: Journal    
DOI: 10.1080/10556780410001709448     Document Type: Article

References (22)

1. Fletcher, R., 1987, Practical Methods of Optimization (2nd edn) (Chichester, England: Wiley).
2. Byrd, R., Liu, D. and Nocedal, J., 1992, On the behaviour of Broyden's class of quasi-Newton methods. SIAM Journal on Optimization, 2, 533-557.
3. Al-Baali, M., 1998, Numerical experience with a class of self-scaling quasi-Newton algorithms. JOTA, 96, 533-553.
4. Powell, M.J.D., 1986, How bad are the BFGS and DFP methods when the objective function is quadratic? Mathematical Programming, 34, 34-47.
5. Zhang, Y. and Tewarson, R.P., 1988, Quasi-Newton algorithms with updates from the preconvex part of Broyden's family. IMA Journal of Numerical Analysis, 8, 487-509.
6. Oren, S.S. and Spedicato, E., 1976, Optimal conditioning of self-scaling variable metric algorithms. Mathematical Programming, 10, 70-90.
7. Nocedal, J. andYuan, Y., 1993, Analysis of a self-scaling quasi-Newton method. Mathematical Programming, 61, 19-37.
8. Oren, S.S. and Luenberger, D.G., 1974, Self-scaling variable metric (SSVM) algorithms I: criteria and sufficient conditions for scaling a class of algorithms. Management Science, 20, 845-862.
9. Al-Baali, M., 1998, Analysis of a family of self-scaling quasi-Newton methods. Computational. Optimization and Applications, 9, 191-203.
10. Byrd, R., Nocedal, J. and Yuan, Y., 1987, Global convergence of a class of quasi-Newton methods on convex problems. SIAM Journal on Numerical Analysis, 24, 1171-1190.
11. Powell, M.J.D., 1976, Some global convergence properties of a variable metric algorithm for minimization without exact line searches. In: R.W. Cottle and C.E. Lemke (Eds) Nonlinear Programming, SIAM-AMS Proceedings, Vol. IX (SIAM Publications).
12. Al-Baali, M., 1995, On measure functions for the self-scaling updating formulae for quasi-Newton methods. Optimization, 32, 59-69.
13. Al-Baali, M. and Khalfan, H., 2003, Globally convergent self-scaling quasi-Newton methods for unconstrained optimization. Technical Report DMCS 1/03, Department of Mathematics and Computer Science, UAE University, United Arab Emirates.
14. Byrd, R.H., Khalfan, H. and Schnabel, R.B., 1996, Analysis of a symmetric rank-one trust region method. SIAM Journal on Optimization, 6, 1025-1039.
15. Conn, A.R., Gould, N.I.M. and Toint, Ph.L., 2000, Trust-Region Methods, MPS-SIAM series on Optimization (Philadelphia, USA).
16. Khalfan, H., Byrd, R.H. and Schnabel, R.B., 1993, A theoretical and experimental study of the symmetric rank one update. SIAM Journal on Optimization, 3, 1-24.
17. Hoshino, S., 1972, A formulation of variable metric methods, Journal of the Institute of Mathematics and Applications, 10, 394-403.
18. Conn, A.R., Gould, N.I.M. and Toint, Ph.L., 1988, Testing a class of methods for solving minimization problems with simple bounds on the variables. Mathematical Computation, 50, 399-430.
19. Fletcher, R. and Powell, M.J.D., 1963, A rapidly convergent descent method for minimization. Computer Journal, 6, 163-168.
20. Grandinetti, L., 1984, Some investigations in anew algorithm for nonlinear optimization based on conic models of the objective function. JOTA, 43, 1-21.
21. Moré, J.J., Garbow, B.S. and Hillstrom, K.E., 1981, Testing unconstrained optimization software. ACM Transactions on Mathematical Software, 7, 17-41.
22. Shanno, D.F. and Phua, K.H., 1978, Matrix conditioning and nonlinear optimization. Mathematical Programming, 14, 149-160.