Skip to main content
SpringerLink
Log in

A note on a sufficient-decrease criterion for a non-derivative step-length procedure

  • Short Communication
  • Published:
Mathematical Programming Submit manuscript

Abstract

A step-length algorithm is an essential part of many descent methods for unconstrained and constrained optimization. In this note we present a criterion that defines an acceptable step length when only function values are available at trial step lengths.

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

References

  1. M. Altman, “Generalized gradient methods of minimizing a functional”,Bulletin de l'Academie Polonaise des Sciences. Série des Sciences Mathématiques, Astronomiques et Physiques 14 (1966) 313–318.

    Google Scholar 

  2. R. Fletcher, “A new approach to variable metric algorithms”,Computer Journal 13 (1970) 317–322.

    Google Scholar 

  3. P.E. Gill and W. Murray, “Safeguarded steplength algorithms for optimization using descent methods”, Tech. Rept. NAC 37, National Physical Laboratory, Teddington, England (1974).

    Google Scholar 

  4. P.E. Gill, W. Murray, M.A. Saunders and M.H. Wright, “Two steplength algorithms for numerical optimization”, Tech. Rept. SOL 79-25, Department of Operations Research, Stanford University, Stanford, CA (1979).

    Google Scholar 

  5. A. Goldstein and J. Price, “An effective algorithm for minimization”,Numerische Mathematik 10 (1967) 184–189.

    Google Scholar 

  6. J.M. Ortega and W.C. Rheinboldt,Iterative solution of nonlinear equations in several variables (Academic Press, London, 1970).

    Google Scholar 

  7. M.J.D. Powell, “A view of unconstrained optimization”, in: L.C.W. Dixon, ed.,Optimization in action (Academic Press, London, 1976) pp. 117–152.

    Google Scholar 

  8. P. Wolfe, “Convergence conditions for ascent methods”,SIAM Review 11 (1969) 226–235.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Systems Optimization Laboratory, Department of Operations Research, Stanford University, 94305, Stanford, CA, USA

    Philip E. Gill, Walter Murray, Michael A. Saunders & Margaret H. Wright

Authors
  1. Philip E. Gill
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Walter Murray
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Michael A. Saunders
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Margaret H. Wright
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This research was supported by the U.S. Department of Energy Contract DE-AC03-76SF00326, PA No. DE-AT03-76ER72018; National Science Foundation Grants MCS-7926009 and ECS-8012974; the Office of Naval Research Contract N00014-75-C-0267; and the U.S. Army Research Office Contract DAAG29-79-C-0110.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gill, P.E., Murray, W., Saunders, M.A. et al. A note on a sufficient-decrease criterion for a non-derivative step-length procedure. Mathematical Programming 23, 349–352 (1982). https://doi.org/10.1007/BF01583799

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01583799

Key words

Search

Navigation