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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.
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Abstract

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Let [An, Bn] be random subintervals of [0, 1] defined recursively as follows. Let A1 = 0, B1 = 1 and take Cn, Dn 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
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

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