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Global optimization using interval analysis: The one-dimensional case

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Abstract

We show how interval analysis can be used to compute the minimum value of a twice continuously differentiable function of one variable over a closed interval. When both the first and second derivatives of the function have a finite number of isolated zeros, our method never fails to find the global minimum.

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Communicated by A. V. Fiacco

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Hansen, E.R. Global optimization using interval analysis: The one-dimensional case. J Optim Theory Appl 29, 331–344 (1979). https://doi.org/10.1007/BF00933139

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Key Words

  • Global optimization
  • interval analysis
  • global minimization
  • one-dimensional optimization