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A Continuation Approach to Global Minimization of Gaussian RBF Models

Seppo Pulkkinen, Marko M. Mäkelä, Napsu Karmitsa, A Continuation Approach to Global Minimization of Gaussian RBF Models. TUCS Technical Reports 998, Turku Centre for Computer Science, 2011.

Abstract:

During the last decade, a lot of research has been devoted to a new class of
derivative-free optimization methods using radial basis function (RBF) models.
Methods of this type usually involve finding a (global) minimizer of the model
function. However, the development of practical methods for solving this
difficult minimization problem has received very little attention in the
literature. In this paper, a new method for global minimization of the Gaussian
RBF model is presented. The proposed method is based on a homotopy continuation
approach. In particular, it is shown that the special structure of the Gaussian
RBF model allows a natural way of using the Gaussian transform as a homotopy
mapping. This integral transformation effectively removes local minima and
preserves the underlying structure of the original RBF model. For tracing the
solution curve of the resulting differential equation, a robust trust
region-based predictor-corrector method is described. Numerical results are
given to demonstrate the reliability of the proposed method.

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BibTeX entry:

@TECHREPORT{tPuMaKa11a,
  title = {A Continuation Approach to Global Minimization of Gaussian RBF Models},
  author = {Pulkkinen, Seppo and Mäkelä, Marko M. and Karmitsa, Napsu},
  number = {998},
  series = {TUCS Technical Reports},
  publisher = {Turku Centre for Computer Science},
  year = {2011},
  keywords = {global optimization, derivative-free optimization, radial basis function, Gaussian transform, continuation method, homotopy, trust region, predictor-corrector method},
  ISBN = {978-952-12-2552-9},
}

Belongs to TUCS Research Unit(s): Other

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