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1 results

  • A note on stochastic search methods for global optimization

  • D. P. Kennedy
  • Journal:
    Advances in Applied Probability / Volume 20 / Issue 2 / June 1988
    Published online by Cambridge University Press:
    01 July 2016, pp. 476-478
    Print publication:
    June 1988
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  • 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.