Convergence Speed of an Integral Method for Computing the Essential Supremum

  • Jens Hichert
  • Armin Hoffmann
  • Hoàng Xuân Phú
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 18)


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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Copyright information

© Springer Science+Business Media Dordrecht 1997

Authors and Affiliations

  • Jens Hichert
    • 1
  • Armin Hoffmann
    • 1
  • Hoàng Xuân Phú
    • 2
  1. 1.Institute of MathematicsTechnical University of IlmenauIlmenauGermany
  2. 2.Institute of MathematicsHanoiVietnam

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