On the properties of convergence of statistical search

Abstract
The convergence of statistical (random) search for the minimization of an arbitrary function Q(w) is treated. It is shown that random search can be regarded as a gradient algorithm in the q-domain. Using this gradient to define the minimum of the function, the convergence is discussed at length-including convergence WP1, convergence in the mean and ε-optimality. The proof of convergence is based upon the theorems of convergence of random processes of Braverman and Rozonoer. The relationship between random search and order statistics is explained. Finally, emphasis is put on the applicability of the theorems for the design of hierarchical search systems and statistical search with a mixture.

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