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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
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Category: math
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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
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Date available: 2008-05-20T18:20:31Z
Last updated: 2015-07-08
Stable URL: http://hdl.handle.net/10338.dmlcz/103990
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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)
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