An adaptive trust region method and its convergence

Science in China, Series A: Mathematics, Physics, Astronomy

Volumn 45, Issue 5, 2002, Pages 620-631

  Zhang, Xiangsun ^a   Zhang, Juliang ^a   Liao, Lizhi ^b  

^a CHINESE ACADEMY OF SCIENCES   (China)

^b HONG KONG BAPTIST UNIVERSITY   (Hong Kong)

Author keywords

Global convergence; Super linear convergence; Trust region method; Unconstrained optimization

Indexed keywords

EID: 0038821465     PISSN: 10069283     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (17)

1. Schnabel, R. B., Eskow, E., A new modified Cholesky factorization, SIAM Journal on Scientific Computing, 1990, 11(6): 1136-1158.
2. Moré, J. J., Recent developments in algorithms and software for trust region methods, in Mathematical Programming: The State of the Art (eds. Bachem, A., Grötchel, M., Korte, B.), Berlin: Springer-Verlag, 1983, 258-287.
3. Powell, M. J. D., Convergence properties of a class minimization algorithms, in Nonlinear Programming 2 (eds. Mangasarian, O. L., Meyer, R. R., Robinson, S. M.), New York: Academic Press, 1975, 1-27.
4. Powell, M. J. D., On the global convergence of trust region algorithms for unconstrained optimization, Mathematical Programming, 1984, 29(3): 297-303.
5. Schultz, G. A., Schnabel, R. B., Byrd, R. H., A family of trust-region-based algorithms for unconstrained minimization with strong global convergence, SIAM Journal on Numerical Analysis, 1985, 22(1): 47-67.
6. Yuan, Y., On the convergence of trust region algorithms, Mathematica Numerica Sinica (in Chinese), 1996, 16(3): 333-346.
7. Yuan, Y., Sun, W., Optimization: Theorem and Algorithm (in Chinese), Beijing: Science Press, 1997.
8. Zhang Xiangsun, Chapter 11: NN models for general nonlinear programming, in Neural Networks in optimization, Dordrecht/Boston/London: Kluwer Academic Publishers, 2000.
9. Byrd, R. H., Schnabel, R. B., Schultz, G. A., Approximate solution of the trust region problem by minimization over two-dimension subspace, Mathematical Programming, 1988, 40(3): 247-263.
10. Gay, D. M., Algorithm 611 subroutine for unconstrained minimization using a model/trust region approach, Transaction of the ACM on Mathematical Software, 1983, 9(4): 503-524.
11. Moré, J. J., Sorensen, D. C., Computing a trust region step, SIAM Journal on Scientific and Statistical Computing, 1983, 4(3): 553-572.
12. Pham Dinh, T., Hoai An, L T., A D.C. optimization algorithm for solving the trust region subproblem, SIAM Journal on Optimization, 1998, 8(2): 476-505.
13. Zhang, J. Z., Xu, C., A class of indefinite dogleg path methods for unconstrained minimization, SIAM Journal on Optimization, 1999, 9(3): 646-667.
14. Nocedal, J., Theory of algorithms for unconstrained optimization, in Acta Numerica 1992 (ed. Iseries, A.), Cambridge: Cambridge University Press, 1992, 199-242.
15. Sartenaer, A., Automatic determination of an initial trust region in nonlinear programming, SIAM Journal on Scientific Computing, 1997, 18(6): 1788-1803.
16. Moré, J. J., Garbow, B. S., Hillstrom, K. E., Testing unconstrained optimization software, Transaction of the ACM on Mathematical Software, 1981, 7(1): 17-41.
17. Nocedal, J., Yuan, Y., Combining trust region and linear search techniques, in Advances in Nonlinear Programming (ed. Yuan, Y.), Dordrecht: Kluwer Academic Publishers, 1996.