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Some effective methods for unconstrained optimization based on the solution of systems of ordinary differential equations

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Abstract

In this paper, we review briefly some methods for minimizing a functionF(x), which proceed by follwoing the solution curve of a system of ordinary differential equations. Such methods have often been thought to be unacceptably expensive; but we show, by means of extensive numerical tests, using a variety of algorithms, that the ODE approach can in fact be implemented in such a way as to be more than competitive with currently available conventional techniques.

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Authors and Affiliations

  1. Numerical Algorithms Group, Oxford, England

    A. A. Brown (Staff Member)

  2. School of Information Science, Hatfield Polytechnic, Hatfield, England

    M. C. Bartholomew-Biggs (Lecturer)

Authors
  1. A. A. Brown
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  2. M. C. Bartholomew-Biggs
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Additional information

Communicated by L. C. W. Dixon

This work was supported by a SERC research studentship for the first author. Both authors are indebted to Dr. J. J. McKeown and Dr. K. D. Patel of SCICON Ltd, the collaborating establishment, for their advice and encouragement.

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Brown, A.A., Bartholomew-Biggs, M.C. Some effective methods for unconstrained optimization based on the solution of systems of ordinary differential equations. J Optim Theory Appl 62, 211–224 (1989). https://doi.org/10.1007/BF00941054

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