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Convergence Speed of an Integral Method for Computing the Essential Supremum

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Part of the Nonconvex Optimization and Its Applications book series (NOIA,volume 18)

Abstract

We give an equivalence between the tasks of computing the essential supremum of a summable function and of finding a certain zero of a one-dimensional convex function. Interpreting the integral method as Newton-type method we show that in the case of objective functions with an essential supremum that is not spread the algorithm can work very slowly. For this reason we propose a method of accelerating the algorithm which is in some respect similar to the method of Aitken/Steffensen.

Key words

  • essential supremum
  • convergence speed
  • integral global optimization
  • Newton algorithm

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© 1997 Springer Science+Business Media Dordrecht

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Hichert, J., Hoffmann, A., Phú, H.X. (1997). Convergence Speed of an Integral Method for Computing the Essential Supremum. In: Bomze, I.M., Csendes, T., Horst, R., Pardalos, P.M. (eds) Developments in Global Optimization. Nonconvex Optimization and Its Applications, vol 18. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-2600-8_10

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  • DOI: https://doi.org/10.1007/978-1-4757-2600-8_10

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-4768-0

  • Online ISBN: 978-1-4757-2600-8

  • eBook Packages: Springer Book Archive