A lower bound on complexity of optimization under the r-fold integrated Wiener measure

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Abstract

We consider the problem of approximating the global minimum of an r-times continuously differentiable function on the unit interval, based on sequentially chosen function and derivative evaluations. Using a probability model based on the r-fold integrated Wiener measure, we establish a lower bound on the expected number of function evaluations required to approximate the minimum to within ∈ on average.

Original languageEnglish (US)
Pages (from-to)404-416
Number of pages13
JournalJournal of Complexity
Volume27
Issue number3-4
DOIs
StatePublished - 2011

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Statistics and Probability
  • Numerical Analysis
  • Mathematics(all)
  • Control and Optimization
  • Applied Mathematics

Keywords

  • Convergence
  • Optimization
  • Statistical models

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