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Empirical Investigation of the Convergence Speed of Inclusion Functions in a Global Optimization Context

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Reliable Computing

Abstract

This paper deals with the empirical convergence speed of inclusion functions applied in interval methods for global optimization. According to our experience the natural interval extension of a given function can be as good as a usual quadratically convergent inclusion function, and although centered forms are in general only of second-order, they can perform as one of larger convergence order. These facts indicate that the theoretical convergence order should not be the only indicator of the quality of an inclusion function, it would be better to know which inclusion function can be used most efficiently in concrete instances. For this reason we have investigated the empirical convergence speed of the usual inclusion functions on some test functions.

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Authors and Affiliations

  1. Research Group on Artificial Intelligence of the Hungarian Academy of Sciences and the University of Szeged, Szeged, Hungary

    Boglárka Tóth

  2. Institute of Informatics, University of Szeged, Szeged, Hungary

    Tibor Csendes

Authors
  1. Boglárka Tóth
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  2. Tibor Csendes
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Corresponding author

Correspondence to Boglárka Tóth.

Additional information

This work has been supported by the Grants OTKA T 034350 and T 032118, OMFB D–30/2000, and OMFB E–24/2001.

The authors are grateful for the anonymous referees for their suggestions.

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Tóth, B., Csendes, T. Empirical Investigation of the Convergence Speed of Inclusion Functions in a Global Optimization Context. Reliable Comput 11, 253–273 (2005). https://doi.org/10.1007/s11155-005-6890-z

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  • DOI: https://doi.org/10.1007/s11155-005-6890-z

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