Title :
A study of alternate stochastic models in Kushner-based global optimization methods
Author :
Perttunen, Cary D.
Author_Institution :
Dept. of Electr. Eng., Louisville Univ., KY, USA
Abstract :
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
Keywords :
optimisation; stochastic processes; Kushner-based global optimization methods; Ornstein-Uhlenbeck process; closed-form solution; drift; fractional Brownian motion; geometric Brownian motion; loss function; n-dimensional simplex-based extension; stochastic models; Brownian motion; Closed-form solution; Covariance matrix; Density functional theory; Gaussian processes; Motion estimation; Optimization methods; Probability density function; Solid modeling; Stochastic processes;
Conference_Titel :
Systems, Man, and Cybernetics, 1991. 'Decision Aiding for Complex Systems, Conference Proceedings., 1991 IEEE International Conference on
Conference_Location :
Charlottesville, VA
Print_ISBN :
0-7803-0233-8
DOI :
10.1109/ICSMC.1991.169750
