Hostname: page-component-6766d58669-nf276 Total loading time: 0 Render date: 2026-05-16T17:45:54.262Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on stochastic search methods for global optimization

Published online by Cambridge University Press:  01 July 2016

D. P. Kennedy
D. P. Kennedy*
Affiliation:
University of Cambridge
*
∗ Postal address: Statistical Laboratory, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB, UK.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

Let [An, Bn ] be random subintervals of [0, 1] defined recursively as follows. Let A 1 = 0, B 1 = 1 and take Cn , D n to be the minimum and maximum of k, i.i.d. random points uniformly distributed on [An, Bn ]. Choose [An+1, Bn+ 1] to be [Cn , Bn ], [Any Dn ] or [Cn , Dn ] with probabilities p, q, r respectively, p + q + r = 1. It is shown that the limiting distribution of [Any Bn ] has the beta distribution on [0,1] with parameters k(p + r) and k(q + r). The result is used to consider a randomized version of Golden Section search.

Keywords

RANDOM BINARY SEARCHRANDOM GOLDEN SECTION SEARCHINTERVAL-REDUCTION TECHNIQUESRANDOMIZED GLOBAL OPTIMIZATION

Information

Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 20 , Issue 2 , June 1988 , pp. 476 - 478
Copyright
Copyright © Applied Probability Trust 1988 

References

[1] Beightler, C. S., Phillips, D. T. and Wilde, D. J. (1979) Foundations of Optimization. Prentice-Hall, Englewood Cliffs, New Jersey.Google Scholar
[2] Chen, R., Lin, E. and Zame, A. (1981) Another arc sine law. Sankhya A 43, 371–373.Google Scholar
[3] Gradshteyn, I. S. and Ryzhik, I. M. (1980) Tables of Integrals, Series and Products. Academic Press, New York.Google Scholar
[4] Van Assche, W. (1986) Products of 2 × 2 stochastic matrices with random entries. J. Appl. Prob. 23, 1019–1024.CrossRefGoogle Scholar
[5] Zemel, E. (1986) Random binary search: a randomizing algorithm for global optimization in ℝ1 . Math. Operat. Res. 11, 651–662.Google Scholar