Average performance of a class of adaptive algorithms for global optimization

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We describe a class of adaptive algorithms for approximating the global minimum of a continuous function on the unit interval. The limiting distribution of the error is derived under the assumption of Wiener measure on the objective functions. For any δ > 0, we construct an algorithm which has error converging to zero at rate n-(1 - δ) in the number of function evaluations n. This convergence rate contrasts with the n11/2 rate of previously studied nonadaptive methods.

Original languageEnglish (US)
Pages (from-to)711-730
Number of pages20
JournalAnnals of Applied Probability
Issue number3
StatePublished - Aug 1997

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Average complexity
  • Brownian motion
  • Global optimization


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