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Journal of Optimization Theory and Applications

, Volume 6, Issue 3, pp 269–282 | Cite as

Numerical experiments on quadratically convergent algorithms for function minimization

  • H. Y. Huang
  • A. V. Levy
Contributed Papers

Abstract

The nine quadratically convergent algorithms for function minimization appearing in Ref. 2 are tested through several numerical examples. A quadratic function and four nonquadratic functions are investigated. For the quadratic function, the results show that, if high-precision arithmetic together with high accuracy in the one-dimensional search is employed, all the algorithms behave identically: they all produce the same sequence of points and they all lead to the minimal point in the same number of iterations (this number is equal at most to the number of variables). For the nonquadratic functions, the results show that some of the algorithms behave identically and, therefore, any one of them can be considered to be representative of the entire class. The effect of different restarting conditions on the convergence characteristics of the algorithms is studied. Proper restarting conditions for faster convergence are given.

Keywords

Numerical Experiment Quadratic Function Fast Convergence Minimal Point Function Minimization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Huang, H. Y., andLevy, A. V.,Numerical Experiments on Quadratically Convergent Algorithms for Function Minimization, Rice University, Aero-Astronautics Report No. 66, 1969.Google Scholar
  2. 2.
    Huang, H. Y.,Unified Approach to Quadratically Convergent Algorithms for Function Minimization, Journal of Optimization Theory and Applications, Vol. 5, No. 6, 1970.Google Scholar
  3. 3.
    Rosenbrock, H. H.,An Automatic Method for Finding the Greatest or the Least Value of a Function, Computer Journal, Vol. 3, No. 3, 1960.Google Scholar
  4. 4.
    Pearson, J. D.,On Variable Metric Methods of Minimization, Research Analysis Corporation, Technical Paper No. RAC-TP-302, 1968.Google Scholar
  5. 5.
    Cragg, E. E., andLevy, A. V.,Study on a Supermemory Gradient Method for the Minimization of Functions, Journal of Optimization Theory and Applications, Vol. 4, No. 3, 1969.Google Scholar
  6. 6.
    Fletcher, R., andPowell, M. J. O.,A Rapidly Convergent Descent Method for Minimization, Computer Journal, Vol. 6, No. 2, 1963.Google Scholar

Copyright information

© Plenum Publishing Corporation 1970

Authors and Affiliations

  • H. Y. Huang
    • 1
  • A. V. Levy
    • 1
  1. 1.Department of Mechanical and Aerospace Engineering and Materials ScienceRice UniversityHouston

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