A conditional Gaussian martingale algorithm for global optimization

Abstract

A new stochastic algorithm for determination of a global minimum of a real valued continuous function defined on K, a compact set of ℝn, having an unique global minimizer in K is introduced and studied, a context discussion is presented and implementations are used to compare the performance of the algorithm with other algorithms. The algorithm may be thought to belong to the random search class but although we use Gaussian distributions, the mean is changed at each step to be the intermediate minimum found at the preceding step and the standard deviations, on the diagonal of the covariance matrix, are halved from one step to the next. The convergence proof is simple relying on the fact that the sequence of intermediate random minima is an uniformly integrable conditional Gaussian martingale. © Springer-Verlag Berlin Heidelberg 2006.