On the convergence of the P-algorithm for one-dimensional global optimization of smooth functions

J. Calvin, A. Žilinskas

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

Abstract

The Wiener process is a widely used statistical model for stochastic global optimization. One of the first optimization algorithms based on a statistical model, the so-called P-algorithm, was based on the Wiener process. Despite many advantages, this process does not give a realistic model for many optimization problems, particularly from the point of view of local behavior. In the present paper, a version of the P-algorithm is constructed based on a stochastic process with smooth sampling functions. It is shown that, in such a case, the algorithm has a better convergence rate than in the case of the Wiener process. A similar convergence rate is proved for a combination of the Wiener model-based P-algorithm with quadratic fit-based local search.

Original languageEnglish (US)
Pages (from-to)479-495
Number of pages17
JournalJournal of Optimization Theory and Applications
Volume102
Issue number3
DOIs
StatePublished - Sep 1999

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

Keywords

  • Gaussian processes
  • Global optimization

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