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Properties and numerical performance of quasi-Newton methods with modified quasi-Newton equations

  • Jianzhong Zhang
  • , Chengxian Xu

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

Abstract

Quasi-Newton (QN) equation plays a core role in contemporary nonlinear optimization. The usual QN equation employs only the gradients, but ignores the available function value information. In this paper, we derive a class of modified QN equations with a vector parameter which use both available gradient and function value information. The modified quasi-Newton methods maintain most properties of the usual quasi-Newton methods, meanwhile they achieve a higher-order accuracy in approximating the second-order curvature of the problem functions than the usual ones do. Numerical experiments are reported which support the theoretical analyses and show the advantages of the modified QN methods over the usual ones. © 2001 Elsevier Science B.V. All rights reserved.
Original languageEnglish
Pages (from-to)269-278
JournalJournal of Computational and Applied Mathematics
Volume137
Issue number2
DOIs
Publication statusPublished - 15 Dec 2001
Externally publishedYes

Bibliographical note

Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

Funding

The research is partially supported by City University of Hong Kong under its Strategic Research Grant #7000944 and the National Natural Science Foundation of China.

Research Keywords

  • Broyden family of updates
  • Curvature approximation
  • Positive-definite update
  • Quasi-Newton equation
  • Superlinear convergence

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