A radial basis function method for global optimization

  • Gutmann H
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Abstract

We introduce a method that aims to find the global minimum of a continuous
nonconvex function on a compact subset of Rd. It is assumed
that function evaluations are expensive and that no additional information
is available. Radial basis function interpolation is used to define
a utility function. The maximizer of this function is the next point
where the objective function is evaluated. We show that, for most
types of radial basis functions that are considered in this paper,
convergence can be achieved without further assumptions on the objective
function. Besides, it turns out that our method is closely related
to a statistical global optimization method, the P-algorithm. A general
framework for both methods is presented. Finally, a few numerical
examples show that on the set of Dixon-Szego test functions our method
yields favourable results in comparison to other global optimization
methods.

Author-supplied keywords

  • global optimization
  • interpolation
  • p-algorithm
  • radial basis functions

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Authors

  • H.-M. Gutmann

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