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Some notes on the quasi-Newton methods
Applications of Mathematics, Tome 27 (1982) no. 6, pp. 433-445
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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.
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.
DOI : 10.21136/AM.1982.103990
Classification : 65H10, 65K05, 90C20, 90C30
Keywords: quasi-Newton methods; unconstrained optimization; conjugate directions; update formulas 
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Ozawa, Masanori; Yanai, Hiroshi. Some notes on the quasi-Newton methods. Applications of Mathematics, Tome 27 (1982) no. 6, pp. 433-445. doi: 10.21136/AM.1982.103990

[1] C. G. Broyden: Quasi-Newton Methods and heir Application to Function Minimisation. Mathematics of Computation, Vol. 21, pp. 368 - 381, (1967). | DOI | MR

[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

[3] W. C. Davidon: Variable Metric Method for Minimization. Argonne National Laboratory Rept. ANL-5990 (Rev.) (1959).

[4] W. C. Davidon: Optimally Conditioned Optimization Algorithms without Line Searches. Mathematical Programming, Vol. 9, pp. 1 - 30, (1975). | DOI | MR | Zbl

[5] J. E. Dennis J. J. Moré: Quasi-Newton Methods, Motivation and Theory. SIAM Review, Vol. 19, pp. 46-89, (1977). | DOI | MR

[6] R. Fletcher: A New Approach to Variable Metric Algorithms. The Computer Journal, Vol. 13, pp. 317-322, (1970). | DOI

[7] R. Fletcher M. J. D. Powell: A Rapidly Convergent Descent Method for Minimization. The Computer Journal, Vol. 6, pp. 163-168, (1963). | DOI | MR

[8] R. Fletcher C. M. Reeves: Function Minimisation by Conjugate Gradients. The Computer Journal, Vol. 7, pp. 149-154, (1964). | DOI | MR

[9] D. Goldfarb: A Family of Variable-Metric Methods Derived by Variational Means. Mathematics of Computation, Vol. 24, pp. 23 - 26, (1970). | DOI | MR | Zbl

[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). | DOI | MR

[11] J. D. Pearson: Variable Metric Methods of Minimisation. The Computer Journal, Vol. 12, pp. 171-179, (1969). | DOI | MR | Zbl

[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). | DOI | MR

[13] D. F. Shanno: Conditioning of Quasi-Newton Methods for Function Minimization. Mathematics of Computation, Vol. 24, pp. 647-657, (1970). | DOI | MR

[14] H. Yanai: On Conjugate Direction Methods. Seminar Report Vol. 190, Institute for Mathematical Sciences, Kyoto Univ., (1973). (In Japanese)

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