A Modification of Davidon's Minimization Method to Accept Difference Approximations of Derivatives

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A Modification of Davidon's Minimization Method to Accept Difference Approximations of Derivatives

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Journal of the ACM (JACM) archive
Volume 14 , Issue 1 (January 1967) table of contents

Pages: 72 - 83

Year of Publication: 1967

ISSN:0004-5411

Author

G. W. Stewart, III

Nuclear Division, Union Carbide Corporation, Oak Ridge, Tennessee

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 3, Downloads (12 Months): 30, Citation Count: 5

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ABSTRACT

A modification of Davidon's method for the unconstrained minimization of a function of several variables is proposed in which the gradient vector is approximated by differences. The step sizes for the differencing are calculated from information available in the course of the minimization and are chosen to approximately balance off the effects of truncation error and cancellation error. Numerical results and comparisons with other methods are given.

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	DAVIDON, W. C. Variable metric method for minimization. AEC Res. Develop. Rep. ANL-5990 (Rev.), 1959.
	2	FLETCHER, R. Function minimization without evaluating derivatives--a review. Comput. J. 8 (1965), 33-41.
	3	-- AND PO'WELL, M. J.D. rapidly convergent descent method for minimization. Comput. J. 6 (1963), 163-168.
	4	-- AND REEVES, C. M. Function minimization by conjugate gradients. Comput. J. 7 (1964), 149-154.
	5	HOUSEHOLDER, A.S. The Theory of Matrices in Numerical Analysis. Blaisdell Publishing Co., New York, 1964, p. 123.
	6	POWELL, M. J.D. An efficient method for finding the minimum of a function of several variables without calculating derivatives. Comput. J. 7 (1964), 155-162.
	7	----. A method for minimizing a sum of squares of nonlinear functions without calculating derivatives. Comput. J. 8 (1965), 303-307.
	8	SmiTH, C.S. The automatic computation of maximum likelihood estimates. NCB Scientific Dep. Rep. S.C. 846/MR/40, 1962.
	9	SWANN, W.H. Report on the development of a new direct search method of optimization. ICI Ltd., Central Instrument Lab. Res, Note 64/3, 1964.

CITED BY 5

	Frank J. Zeleznik, Quasi- Newton Methods for Nonlinear Equations, Journal of the ACM (JACM), v.15 n.2, p.265-271, April 1968
	Gerald Berman, Lattice Approximations to the Minima of Functions of Several Variables, Journal of the ACM (JACM), v.16 n.2, p.286-294, April 1969
	M. J. D. Powell, A View of Unconstrained Minimization Algorithms that Do Not Require Derivatives, ACM Transactions on Mathematical Software (TOMS), v.1 n.2, p.97-107, June 1975
	David M. Gay, Algorithm 611: Subroutines for Unconstrained Minimization Using a Model/Trust-Region Approach, ACM Transactions on Mathematical Software (TOMS), v.9 n.4, p.503-524, Dec. 1983
	J. E. Dennis, Jr., Algorithms for nonlinear problems which use discrete approximations to derivatives, Proceedings of the 1971 26th annual conference, p.446-456, January 1971