Global Optimization

  • Ulrich Kulisch
  • Rolf Hammer
  • Dietmar Ratz
  • Matthias Hocks
Part of the Springer Series in Computational Mathematics book series (SSCM, volume 21)

Abstract

We want to find the global minimum in an interval [x] of a function f that may have many local minima. We want to compute the minimum value of f and the point(s) at which the minimum value is attained. This is a very difficult problem for classical methods because narrow, deep valleys may escape detection. In contrast, the interval method presented here evaluates f on a continuum of points, including those points that are not finitely representable, so valleys, no matter how narrow, are recognized with certainty. Further, interval techniques often can reject large regions in which the optimum can be guaranteed not to lie, so they can be faster overall than classical methods for many problems.

Keywords

Assure Veri Terion 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Ulrich Kulisch
    • 1
  • Rolf Hammer
    • 1
  • Dietmar Ratz
    • 1
  • Matthias Hocks
    • 1
  1. 1.Institut für Angewandte MathematikUniversität KarlsruheKarlsruheGermany

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