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Square-root variable-metric methods for minimization

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Variable-metric methods are presented which do not need an accurate one-dimensional search and eliminate roundoff error problems which can occur in updating the metric for large-dimension systems. The methods are based on updating the square root of the metric, so that a positive-definite metric always results. The disadvantage of intentionally relaxing the accuracy of the one-dimensional search is that the number of iterations (and hence, gradient evaluations) increases. For problems involving a large number of variables, the square-root method is presented in a triangular form to reduce the amount of computation. Also, for usual optimization problems, the square-root procedure can be carried out entirely in terms of the metric, eliminating storage and computer time associated with computations of the square root of the metric.

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Communicated by H. Y. Huang

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Hull, D.G., Tapley, B.D. Square-root variable-metric methods for minimization. J Optim Theory Appl 21, 251–259 (1977). https://doi.org/10.1007/BF00933529

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Key Words

  • Nonlinear programming
  • variable-metric methods
  • parameter optimization
  • function minimization
  • mathematical programming