Generalized subinterval selection criteria for interval global optimization

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12 Citations (Scopus)

Abstract

The convergence properties of interval global optimization algorithms are studied which select the next subinterval to be subdivided with the largest value of the indicator pf(f k,X)=(f k-F(X))/(F(X)-F(X)). This time the more general case is investigated, when the global minimum value is unknown, and thus its estimation f k in the iteration k has an important role. A sharp necessary and sufficient condition is given on the f k values approximating the global minimum value that ensure convergence of the optimization algorithm. The new theoretical result enables new, more efficient implementations that utilize the advantages of the pf * based interval selection rule, even for the more general case when no reliable estimation of the global minimum value is available.

Original languageEnglish
Pages (from-to)93-100
Number of pages8
JournalNumerical Algorithms
Volume37
Issue number1-4 SPEC. ISS.
DOIs
Publication statusPublished - Dec 1 2004

Keywords

  • convergence properties
  • global optimization
  • interval methods
  • interval selection

ASJC Scopus subject areas

  • Applied Mathematics

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