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Computational schemes of the Davidon-Fletcher-Powell method in infinite-dimensional space

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Abstract

The disadvantage of the extension of the Davidon-Fletcher-Powell method to infinite-dimensional space is that the information to be stored in the computer increases with the number of iterations. In this paper, a computational scheme is proposed to remove this disadvantage and make the extension method more practicable. The linear operator which determines the direction of one-dimensional search in the method is formulated by integral kernels to derive the scheme. Furthermore, polynomial interpolation methods are proposed to save computer storage. The computational scheme which is presented here and the polynomial interpolation method are successfully applied to an optimal control problem.

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References

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Authors and Affiliations

  1. Department of Iron and Steel Engineering, Faculty of Engineering, Nagoya University, Nagoya, Japan

    K. Oi (Lecturer)

  2. Department of Industrial and Mechanical Engineering, School of Engineering, Okayama University, Okayama, Japan

    H. Sayama (Professor)

  3. Department of Chemical Engineering, Faculty of Engineering, Kyoto University, Kyoto, Japan

    T. Takamatsu (Professor)

Authors
  1. K. Oi
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  2. H. Sayama
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  3. T. Takamatsu
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Additional information

Communicated by M. R. Hestenes

The authors would like to thank Dr. N. Adachi for valuable discussion. Computations were carried out at the computing centers of Osaka University, Kyoto University, and Tokyo University.

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Oi, K., Sayama, H. & Takamatsu, T. Computational schemes of the Davidon-Fletcher-Powell method in infinite-dimensional space. J Optim Theory Appl 12, 447–458 (1973). https://doi.org/10.1007/BF00935240

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  • DOI: https://doi.org/10.1007/BF00935240

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