A Kiefer-Wolfowitz algorithm with randomized differences

A Kiefer-Wolfowitz or simultaneous perturbation algorithm that uses either one-sided or two-sided randomized differences and truncations at randomly v arying bounds is given in this paper. At each iteration of the algorithm on ly two observations are required in contrast to 2l observations, where l is the dimension, in the classical algorithm, The algorithm given here is sho wn to he convergent under only some mild conditions. A rate of convergence and an asymptotic normality of the algorithm are also established.