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