Skip to main content
SpringerLink
Log in

Unified approach to quadratically convergent algorithms for function minimization

  • Contributed Papers
  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

In this paper, a unified method to construct quadratically convergent algorithms for function minimization is described. With this unified method, a generalized algorithm is derived. It is shown that all the existing conjugate-gradient algorithms and variable-metric algorithms can be obtained as particular cases. In addition, several new practical algorithms can be generated. The application of these algorithms to quadratic functions as well as nonquadratic functions is discussed.

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. Huang, H. Y.,Unified Approach to Quadratically Convergent Algorithms for Function Minimization, Rice University, Aero-Astronautics Report No. 64, 1969.

  2. Hestenes, M. R., andStiefel, E.,Methods of Conjugate Gradients for Solving Linear Systems, Journal of Research of the National Bureau of Standards, Vol. 49, No. 6, 1952.

  3. Fletcher, R., andReeves, C. M.,Function Minimization by Conjugate Gradients, Computer Journal, Vol. 7, No. 2, 1964.

  4. Beckman, F. S.,The Solution of Linear Equation by the Conjugate Gradient Method, Mathematical Methods for Digital Computers, Edited by A. Ralston and H. S. Wilf, John Wiley and Sons, New York, 1960.

    Google Scholar 

  5. Miele, A., andCantrell, J. W.,Study on a Memory Gradient Method for the Minimization of Functions, Journal of Optimization Theory and Applications, Vol. 3, No. 6, 1969.

  6. Cantrell, J. W.,Relation between the Memory Gradient Method and the Fletcher-Reeves Method, Journal of Optimization Theory and Applications, Vol. 4, No. 1, 1969.

  7. Davidon, W. C.,Variable Metric Method for Minimization, Argonne National Laboratory, Report No. ANL-5990, 1959.

  8. Fletcher, R., andPowell, M. J. D.,A Rapidly Convergent Descent Method for Minimization, Computer Journal, Vol. 6, No. 2, 1963.

  9. Pearson, J. D.,On Variable Metric Methods of Minimization, Research Analysis Corporation, Technical Paper No. RAC-TP-302, 1968.

  10. Huang, H. Y., andLevy, A. V.,Numerical Experiments on Quadratically Convergent Algorithms for Function Minimization, Rice University, Aero-Astronautics Report No. 66, 1969.

Additional bibliography

  1. Myers, G.,Properties of the Conjugate-Gradient and Davidon Methods, Journal of Optimization Theory and Applications, Vol. 2, No. 4, 1968.

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering and Materials Science, Rice University, Houston, Texas

    H. Y. Huang (Assistant Professor of Astronautics)

Authors
  1. H. Y. Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by A. Miele

This research, supported by the Office of Scientific Research, Office of Aerospace Research, United States Air Force, Grant No. AF-AFOSR-828-67, is based on Ref. 1.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Huang, H.Y. Unified approach to quadratically convergent algorithms for function minimization. J Optim Theory Appl 5, 405–423 (1970). https://doi.org/10.1007/BF00927440

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00927440

Keywords

Search

Navigation