A study of alternate stochastic models in Kushner-based global optimization methods

The use of alternative stochastic models (other than the Brownian motion process) in conjunction with H.J. Kushner's loss function (1963) is explored. The following stochastic process models are considered: the process of G.E. Uhlenbeck and L.S. Ornstein (1930); Brownian motion with drift; geometric Brownian motion; and fractional Brownian motion. The geometric Brownian motion model is shown to be the most attractive of the selections since a closed-form solution exists, an n-dimensional simplex-based extension can be developed, and no parameters need to be estimated or prespecified. It is also shown that the Ornstein-Uhlenbeck process and fractional Brownian motion yield searches equivalent to the standard Brownian method for limiting values of their parameters.<
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