Skip to main content
SpringerLink
Log in

Local and superlinear convergence of a class of variable metric methods

Lokale und superlineare Konvergenz einer Klasse von Verfahren mit variabler Metrik

  • Published:
Computing Aims and scope Submit manuscript

Abstract

This paper considers a class of variable metric methods for unconstrained minimization problems. It is shown that with a step size of one each member of this class converges locally and superlinearly.

Zusammenfassung

In dieser Arbeit wird eine Klasse von Verfahren mit variabler Metrik zur Minimierung von Funktionen ohne Nebenbedingungen untersucht. Es wird gezeigt, daß jede dieser Methoden unter Benutzung der Schrittweite eins lokal und superlinear konvergiert.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Broyden, C. G.: Quasi-Newton methods and their application to function minimization. Mathematics of Computation21, 368–381 (1967).

    Google Scholar 

  2. Broyden, C. G.: The convergence of a class of double-rank minimization algorithms. Parts 1 and 2. Journal of the Institute of Mathematics and its Applications6, 76–90, 222–231 (1970).

    Google Scholar 

  3. Broyden, C. G., Dennis, J. E. Jr., Moré, J. J.: On the local and superlinear convergence of quasi-Newton methods. Journal of the Institute of Mathematics and its Applciations12, 223–245 (1973).

    Google Scholar 

  4. Davidon, W. C.: Variable metric methods for minimization. Argonne National Laboratories rept. ANL-5990 (1959).

  5. Fletcher, R., Powell, M. J. D.: A rapidly convergent descent method for minimization. The Computer Journal6, 163–168 (1963).

    Google Scholar 

  6. Fletcher, R.: A new approach to variable metric algorithms. The Computer Journal13, 317–322 (1970).

    Google Scholar 

  7. Goldfarb, D.: A family of variable metric methods derived by variational means. Mathematics of Computation24, 23–26 (1970).

    Google Scholar 

  8. Huang, H. Y.: Unified approach to quadratically convergent algorithms for function minimization. Journal of Optimization Theory and Applications5, 405–423 (1970).

    Google Scholar 

  9. Ritter, K.: Global and superlinear convergence of a class of variable metric methods. Mathematics Research Center TSR No. 1945, University of Wisconsin-Madison, 1979.

  10. Shanno, D. F.: Conditioning of quasi-Newton methods for function minimization. Mathematics of Computation24, 647–656 (1970).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematisches Institut A, Universität Stuttgart, Pfaffenwaldring 57/9, D-7000, Stuttgart 80, Federal Republic of Germany

    K. Ritter

Authors
  1. K. Ritter
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ritter, K. Local and superlinear convergence of a class of variable metric methods. Computing 23, 287–297 (1979). https://doi.org/10.1007/BF02252133

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02252133

Keywords

Search

Navigation