A note on stochastic search methods for global optimization
Douglas P. Kennedy · Advances in Applied Probability · 1988
Let [ A n , B n ] be random subintervals of [0, 1] defined recursively as follows. Let A 1 = 0, B 1 = 1 and take C n , D n to be the minimum and maximum of k, i.i.d. random points uniformly distributed on [ A n , B n ]. Choose [ A n+1 , B n+ 1 ] to be [ C n , B n ] , [ A ny D n ] or [ C n , D n ] with probabilities p, q, r respectively, p + q + r = 1. It is shown that the limiting distribution of [ A ny B n ] 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.