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 varying bounds is given in this paper. At each iteration of the algorithm only two observations are required in contrast to 2` observations, where ` is the dimension, in the classical algorithm. The algorithm given here is shown to be convergent under only some mild conditions. A rate of convergence and an asymptotic normality of the algorithm are also established.