无约束最优化问题随机搜索算法的收敛性

引言 设F(X)是定义在n维欧氏空间R~n上的实值连续函数,欲求它的极小点和极小值。解这样的无约束极值问题,已提出了好几种随机搜索算法。这类算法简单直观,适用范围广泛,是人们时常采用的方法之一。但是对这类算法的收敛理论,迄今研究甚少。 G.Schrack和N.Borowski对三种比较流行的随机搜索算法作了系统的计算实验,[2]说明M.A.Schumer和K.Steiglitz在[3]中提出的“调整步长随机搜索”算法(Ada-ptive step size random search)其计算效果比较好。本文在目标函数F(X)的一定假设条件下证明了这种算法的收敛性。

THE CONVERGENCE OF A RANDOM SEARCH ALGORITHM FOR UNCONSTRAINED OPTIMIZATION PROBLEMS

A number of random search algorithms have been proposed for calculating the least va-lue of a function F(X). Numerical experiment shows that adaptive step size random sear-ch algorithm (Schumer and Steiglitz [3]) is comparatively efficient. This algorithm, howe-ver, has not been analysed theoretically. In this paper, the author proves its convergenceproperty with the aid of the theory of Markov processes.