On Convergence of a P-Algorithm Based on a Statistical Model of Continuously Differentiable Functions

James M. Calvin, Antanas Žilinskas

Research output: Contribution to journalConference articlepeer-review

Abstract

This paper is a study of the one-dimensional global optimization problem for continuously differentiable functions. We propose a variant of the so-called P-algorithm, originally proposed for a Wiener process model of an unknown objective function. The original algorithm has proven to be quite effective for global search, though it is not efficient for the local component of the optimization search if the objective function is smooth near the global minimizer. In this paper we construct a P-algorithm for a stochastic model of continuously differentiable functions, namely the once-integrated Wiener process. This process is continuously differentiable, but nowhere does it have a second derivative. We prove convergence properties of the algorithm.

Original languageEnglish (US)
Pages (from-to)229-245
Number of pages17
JournalJournal of Global Optimization
Volume19
Issue number3
DOIs
StatePublished - Mar 2001
EventInternational Workshop on Global Optimization - Firenze, Italy
Duration: Sep 28 1999Oct 2 1999

All Science Journal Classification (ASJC) codes

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

Keywords

  • Global optimization
  • Statistical models
  • Wiener process

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