Multivariate stochastic approximation using a simultaneous perturbation gradient approximation

Consider the problem of finding a root of the multivariate gradient equation that arises in function minimization. When only noisy measurements of the function are available, a stochastic approximation (SA) algorithm of the general Kiefer–Wolfowitz type is appropriate for estimating the root. This paper presents an SA algorithm that is based on a ‘simultaneous perturbation’ gradient approximation instead of the standard finite difference approximation of Kiefer–Wolfowitz type procedures. Theory and numerical experience indicate that the algorithm presented here can be significantly more efficient than the standard finite difference-based algorithms in large-dimensional problems.