Skip to main content
SpringerLink
Log in

A combined variable metric — Conjugate Gradient algorithm for a class of large scale unconstrained minimization problems

  • Nonlinear And Stochastic Programming
  • Conference paper
  • First Online:
Book cover Optimization Techniques

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 7))

Abstract

An algorithm is being presented for a special class of unconstrained minimization problems. The algorithm exploits the special structure of the Hessian in the problems under consideration. It is based on applying Bertsekas' [1] Scaled Partial Conjugate Gradient method with respect to a metric that is updated by the Rank One update, using gradients obtained in the preceeding steps. Two classes of problems are presented having the structure assumed in designing the proposed algorithm. In both cases the algorithm uses only first derivative information. Furthermore, it possesses quadratic termination in considerably fewer steps than the number of variables.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bertsekas, D. P., "Partial Conjugate Gradient Methods for a Class of Optimal Control Problems", IEEE Transaction on Automatic Control, Vol. AC-19, pp. 209–217, 1974.

    Google Scholar 

  2. Broyden, C. G., "Quasi-Newton Methods and Their Application to Function Minimization", Math. Comp., Vol. 21, pp 368–381, 1967.

    Google Scholar 

  3. Cullum, Jane and Brayton, R. K., Some Remarks on the Symmetric Rank One Update, IBM Research Center Report 6157, Yorktown Heights, New York, 1976.

    Google Scholar 

  4. Davidon, W. C., "Variable Metric Method for Minimization," A.E.C. Research and Development Rep. ANL-5990 (Rev.), 1959.

    Google Scholar 

  5. Fletcher, R. and Powell, M. J. D., "A Rapidly Convergent Descent Method for Minimization", Comp. Jnl., Vol. 6, pp. 163–168, 1963.

    Google Scholar 

  6. Fletcher, R. and Reeves, C. M., "Function Minimization by Conjugate Gradients", Comp. Jnl., Vol. 7, pp. 149–154, 1964.

    Google Scholar 

  7. Luenberger, D. G., "Introduction to Linear and Nonlinear Programming", Reading, Mass: Addison-Wesley 1973.

    Google Scholar 

  8. Murtagh, B. A. and R. W. H. Sargent, Computational Experience with Quadratically Convergent Minimization Methods, Comp. Jnl. 13, 185–194, 1970.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Xerox Palo Alto Research Center, 3333 Coyote Hill Road, Palo Alto, California

    Shmuel S. Oren

Authors
  1. Shmuel S. Oren
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

J. Stoer

Rights and permissions

Reprints and permissions

Copyright information

© 1978 Springer-Verlag

About this paper

Cite this paper

Oren, S.S. (1978). A combined variable metric — Conjugate Gradient algorithm for a class of large scale unconstrained minimization problems. In: Stoer, J. (eds) Optimization Techniques. Lecture Notes in Control and Information Sciences, vol 7. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0006515

Download citation

  • DOI: https://doi.org/10.1007/BFb0006515

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08708-3

  • Online ISBN: 978-3-540-35890-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation