Extended conjugate-gradient methods with restarts

  • W. R. Boland
  • J. S. Kowalik
Contributed Papers


Three variants of the classical conjugate-gradient method are presented. Two of these variants are based upon a nonlinear function of a quadratic form. A restarting procedure due to Powell, and based upon some earlier work of Beale, is discussed and incorporated into two of the variants. Results of applying the four algorithms to a set of benchmark problems are included, and some tentative conclusions about the relative merits of the four schemes are presented.

Key Words

Nonlinear optimization conjugate-gradient methods numerical methods computing methods mathematical programming nonlinear programming 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Powell, M. J. D.,Some Convergence Properties of the Conjugate Gradient Method, Mathematical Programming, Vol. 11, pp. 42–49, 1976.Google Scholar
  2. 2.
    Boland, W. R., Kamgnia, E. R., andKowalik, J. S.,A Conjugate Gradient Optimization Method Invariant to Nonlinear Scaling, Journal of Optimization Theory and Applications, Vol. 27, No. 2, 1979.Google Scholar
  3. 3.
    Fried, I.,N-step Conjugate Gradient Minimization Scheme for Nonquadratic Functions, AIAA Journal, Vol. 9, pp. 2286–2287, 1971.Google Scholar
  4. 4.
    Spedicato, E.,A Variable Metric Method for Function Minimization Derived from Invariancy to Nonlinear Scaling, Journal of Optimization Theory and Applications, Vol. 20, pp. 315–329, 1976.Google Scholar
  5. 5.
    Powell, M. J. D.,Restart Procedures for the Conjugate Gradient Method, Atomic Energy Research Establishment, Harwell, England, Report No. CSS-24, 1975.Google Scholar
  6. 6.
    Beale, E. M. L.,A Derivation of Conjugate Gradients, Numerical Methods for Nonlinear Optimization, Edited by F. A. Lootsma, Academic Press, New York, New York, pp. 39–44, 1972.Google Scholar

Additional Bibliography

  1. 7.
    Spedicato, E.,Recent Developments in the Variable Metric Method for Nonlinear Unconstrained Optimization, Towards Global Optimization, Edited by L. W. Dixon and G. P. Szegö, North-Holland, Amsterdam, pp. 182–195, 1975.Google Scholar

Copyright information

© Plenum Publishing Corporation 1979

Authors and Affiliations

  • W. R. Boland
    • 1
  • J. S. Kowalik
    • 2
  1. 1.Department of Mathematical SciencesClemson UniversityClemson
  2. 2.Department of Computer ScienceWashington State UniversityPullman

Personalised recommendations