Global Optimization

Ulrich Kulisch, Rolf Hammer, Matthias Hocks and Dietmar Ratz
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Ulrich Kulisch: Universität Karlsruhe, Institut für Angewandte Mathematik
Rolf Hammer: Universität Karlsruhe, Institut für Angewandte Mathematik
Matthias Hocks: Universität Karlsruhe, Institut für Angewandte Mathematik
Dietmar Ratz: Universität Karlsruhe, Institut für Angewandte Mathematik

Chapter Chapter 7 in C++ Toolbox for Verified Computing I, 1995, pp 113-139 from Springer

Abstract: 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 represent able, 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: Global Optimization; Global Minimizer; Interval Arithmetic; Global Optimization Method; Interval Vector (search for similar items in EconPapers)
Date: 1995
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DOI: 10.1007/978-3-642-79651-7_7

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