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Developments in Global Optimization pp 153–170Cite as

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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  • DOI: 10.1007/978-1-4757-2600-8_10
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Author information

Authors and Affiliations

  1. Institute of Mathematics, Technical University of Ilmenau, PF 0565, D-98684, Ilmenau, Germany

    Jens Hichert & Armin Hoffmann

  2. Institute of Mathematics, P. O. Box 631, Bo Ho, 10000, Hanoi, Vietnam

    Hoàng Xuân Phú

Authors
  1. Jens Hichert
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  2. Armin Hoffmann
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  3. Hoàng Xuân Phú
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Editor information

Editors and Affiliations

  1. University of Vienna, Vienna, Austria

    Immanuel M. Bomze

  2. József Attila University, Szeged, Hungary

    Tibor Csendes

  3. University of Trier, Trier, Germany

    Reiner Horst

  4. University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos

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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

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