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Mathematical Programming

, Volume 37, Issue 1, pp 59–80 | Cite as

Bayesian stopping rules for multistart global optimization methods

  • C. G. E. Boender
  • A. H. G. Rinnooy Kan
Article

Abstract

By far the most efficient methods for global optimization are based on starting a local optimization routine from an appropriate subset of uniformly distributed starting points. As the number of local optima is frequently unknown in advance, it is a crucial problem when to stop the sequence of sampling and searching. By viewing a set of observed minima as a sample from a generalized multinomial distribution whose cells correspond to the local optima of the objective function, we obtain the posterior distribution of the number of local optima and of the relative size of their regions of attraction. This information is used to construct sequential Bayesian stopping rules which find the optimal trade off between reliability and computational effort.

Key words

Global optimization multistart methods clustering methods Bayesian stopping rules multinomial distribution 

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Copyright information

© The Mathematical Programming Society, Inc. 1987

Authors and Affiliations

  • C. G. E. Boender
    • 1
  • A. H. G. Rinnooy Kan
    • 2
    • 3
  1. 1.Econometric InstituteErasmus UniversityRotterdamThe Netherlands
  2. 2.Econometric InstituteErasmus UniversityRotterdamThe Netherlands
  3. 3.Department of Industrial Engineering & Operations Research, School of Business AdministrationUniversity of CaliforniaBerkeleyUSA

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