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On variable-metric algorithms

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Abstract

In this paper, a generalized variable-metric algorithm is presented. It is shown that this algorithm attains the minimum of a positive-definite, quadratic function in a finite number of steps and that thevariable-metric matrix tends to the inverse of the Hessian matrix. Most known variable-metric algorithms can be derived from this generalized algorithm, and some new algorithms are also obtained.

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Additional information

The author expresses his gratitude to Professor H. Tokumaru for guidance and encouragement.

Communicated by A. Miele

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Adachi, N. On variable-metric algorithms. J Optim Theory Appl 7, 391–410 (1971). https://doi.org/10.1007/BF00931977

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Keywords

  • Finite Number
  • Generalize Algorithm
  • Quadratic Function
  • Hessian Matrix