Some notes on the quasi-Newton methods

Masanori Ozawa; Hiroshi Yanai

Aplikace matematiky (1982)

  • Volume: 27, Issue: 6, page 433-445
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Ozawa, Masanori, and Yanai, Hiroshi. "Some notes on the quasi-Newton methods." Aplikace matematiky 27.6 (1982): 433-445. <http://eudml.org/doc/15264>.

@article{Ozawa1982,
abstract = {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.},
author = {Ozawa, Masanori, Yanai, Hiroshi},
journal = {Aplikace matematiky},
keywords = {quasi-Newton methods; unconstrained optimization; conjugate directions; update formulas; quasi-Newton methods; unconstrained optimization; conjugate directions; update formulas},
language = {eng},
number = {6},
pages = {433-445},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some notes on the quasi-Newton methods},
url = {http://eudml.org/doc/15264},
volume = {27},
year = {1982},
}

TY - JOUR
AU - Ozawa, Masanori
AU - Yanai, Hiroshi
TI - Some notes on the quasi-Newton methods
JO - Aplikace matematiky
PY - 1982
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 27
IS - 6
SP - 433
EP - 445
AB - 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.
LA - eng
KW - quasi-Newton methods; unconstrained optimization; conjugate directions; update formulas; quasi-Newton methods; unconstrained optimization; conjugate directions; update formulas
UR - http://eudml.org/doc/15264
ER -

References

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  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). (1970) MR0433870
  3. W. C. Davidon, Variable Metric Method for Minimization, Argonne National Laboratory Rept. ANL-5990 (Rev.) (1959). (1959) 
  4. W. C. Davidon, 10.1007/BF01681328, Mathematical Programming, Vol. 9, pp. 1 - 30, (1975). (1975) Zbl0328.90055MR0383741DOI10.1007/BF01681328
  5. J. E. Dennis J. J. Moré, 10.1137/1019005, SIAM Review, Vol. 19, pp. 46-89, (1977). (19,) MR0445812DOI10.1137/1019005
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  7. R. Fletcher M. J. D. Powell, 10.1093/comjnl/6.2.163, The Computer Journal, Vol. 6, pp. 163-168, (1963). (1963) MR0152116DOI10.1093/comjnl/6.2.163
  8. R. Fletcher C. M. Reeves, 10.1093/comjnl/7.2.149, The Computer Journal, Vol. 7, pp. 149-154, (1964). (1964) MR0187375DOI10.1093/comjnl/7.2.149
  9. D. Goldfarb, 10.1090/S0025-5718-1970-0258249-6, Mathematics of Computation, Vol. 24, pp. 23 - 26, (1970). (1970) Zbl0196.18002MR0258249DOI10.1090/S0025-5718-1970-0258249-6
  10. H. Y. Huang, 10.1007/BF00927440, Journal of Optimization Theory and Applications, Vol. 5, pp. 405 - 423, (1970). (1970) MR0288939DOI10.1007/BF00927440
  11. J. D. Pearson, 10.1093/comjnl/12.2.171, The Computer Journal, Vol. 12, pp. 171-179, (1969). (1969) Zbl0207.17301MR0242355DOI10.1093/comjnl/12.2.171
  12. M. J. D. Powell, 10.1093/comjnl/7.2.155, The Computer Journal, Vol. 7, pp. 155-162, (1964). (1964) MR0187376DOI10.1093/comjnl/7.2.155
  13. D. F. Shanno, 10.1090/S0025-5718-1970-0274029-X, Mathematics of Computation, Vol. 24, pp. 647-657, (1970). (1970) MR0274029DOI10.1090/S0025-5718-1970-0274029-X
  14. H. Yanai, On Conjugate Direction Methods, Seminar Report Vol. 190, Institute for Mathematical Sciences, Kyoto Univ., (1973). (In Japanese) (190,) 

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