| Title:
|
Some notes on the quasi-Newton methods (English) |
| Author:
|
Ozawa, Masanori |
| Author:
|
Yanai, Hiroshi |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
27 |
| Issue:
|
6 |
| Year:
|
1982 |
| Pages:
|
433-445 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
A survey note whose aim is to establish the heuristics and natural relations in a class of Quasi-Newton methods in optimization problems. It is shown that a particular algorithm of the class is specified by characcterizing some parameters (scalars and matrices) in a general solution of a matrix equation. (English) |
| Keyword:
|
quasi-Newton methods |
| Keyword:
|
unconstrained optimization |
| Keyword:
|
conjugate directions |
| Keyword:
|
update formulas |
| MSC:
|
65H10 |
| MSC:
|
65K05 |
| MSC:
|
90C20 |
| MSC:
|
90C30 |
| idZBL:
|
Zbl 0516.65040 |
| idMR:
|
MR0678113 |
| DOI:
|
10.21136/AM.1982.103990 |
| . |
| Date available:
|
2008-05-20T18:20:31Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103990 |
| . |
| Reference:
|
[1] C. G. Broyden: Quasi-Newton Methods and heir Application to Function Minimisation.Mathematics of Computation, Vol. 21, pp. 368 - 381, (1967). MR 0224273, 10.1090/S0025-5718-1967-0224273-2 |
| Reference:
|
[2] C. G. Broyden: The Convergence of a Class of Double-Rank Minimisation Algorithms.Journal of the Institute of Mathematics and its Applications, Vol. 6, pp. 79-90, 222-231 (1970). MR 0433870 |
| Reference:
|
[3] W. C. Davidon: Variable Metric Method for Minimization.Argonne National Laboratory Rept. ANL-5990 (Rev.) (1959). |
| Reference:
|
[4] W. C. Davidon: Optimally Conditioned Optimization Algorithms without Line Searches.Mathematical Programming, Vol. 9, pp. 1 - 30, (1975). Zbl 0328.90055, MR 0383741, 10.1007/BF01681328 |
| Reference:
|
[5] J. E. Dennis J. J. Moré: Quasi-Newton Methods, Motivation and Theory.SIAM Review, Vol. 19, pp. 46-89, (1977). MR 0445812, 10.1137/1019005 |
| Reference:
|
[6] R. Fletcher: A New Approach to Variable Metric Algorithms.The Computer Journal, Vol. 13, pp. 317-322, (1970). 10.1093/comjnl/13.3.317 |
| Reference:
|
[7] R. Fletcher M. J. D. Powell: A Rapidly Convergent Descent Method for Minimization.The Computer Journal, Vol. 6, pp. 163-168, (1963). MR 0152116, 10.1093/comjnl/6.2.163 |
| Reference:
|
[8] R. Fletcher C. M. Reeves: Function Minimisation by Conjugate Gradients.The Computer Journal, Vol. 7, pp. 149-154, (1964). MR 0187375, 10.1093/comjnl/7.2.149 |
| Reference:
|
[9] D. Goldfarb: A Family of Variable-Metric Methods Derived by Variational Means.Mathematics of Computation, Vol. 24, pp. 23 - 26, (1970). Zbl 0196.18002, MR 0258249, 10.1090/S0025-5718-1970-0258249-6 |
| Reference:
|
[10] H. Y. Huang: A Unified Approach to Quadratically Convergent Algorithms for Function Minimisation.Journal of Optimization Theory and Applications, Vol. 5, pp. 405 - 423, (1970). MR 0288939, 10.1007/BF00927440 |
| Reference:
|
[11] J. D. Pearson: Variable Metric Methods of Minimisation.The Computer Journal, Vol. 12, pp. 171-179, (1969). Zbl 0207.17301, MR 0242355, 10.1093/comjnl/12.2.171 |
| Reference:
|
[12] M. J. D. Powell: An Efficient Method of Finding the Minimum of a Function of Several Variables without Calculating Derivatives.The Computer Journal, Vol. 7, pp. 155-162, (1964). MR 0187376, 10.1093/comjnl/7.2.155 |
| Reference:
|
[13] D. F. Shanno: Conditioning of Quasi-Newton Methods for Function Minimization.Mathematics of Computation, Vol. 24, pp. 647-657, (1970). MR 0274029, 10.1090/S0025-5718-1970-0274029-X |
| Reference:
|
[14] H. Yanai: On Conjugate Direction Methods.Seminar Report Vol. 190, Institute for Mathematical Sciences, Kyoto Univ., (1973). (In Japanese) |
| . |
