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Multivariate stochastic approximation using a simultaneous perturbation gradient approximation

IEEE Transactions on Automatic Control · 1992 · Vol. 37(3) · pp. 332–341

James C. Spall✉(Johns Hopkins University Applied Physics Laboratory)

Abstract

The problem of finding a root of the multivariate gradient equation that arises in function minimization is considered. When only noisy measurements of the function are available, a stochastic approximation (SA) algorithm for the general Kiefer-Wolfowitz type is appropriate for estimating the root. The paper presents an SA algorithm that is based on a simultaneous perturbation gradient approximation instead of the standard finite-difference approximation of Keifer-Wolfowitz type procedures. Theory and numerical experience indicate that the algorithm can be significantly more efficient than the standard algorithms in large-dimensional problems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>

Probabilistic and Robust Engineering Design Gaussian Processes and Bayesian Inference Advanced Multi-Objective Optimization AlgorithmsStochastic approximationSimultaneous perturbation stochastic approximationApproximation algorithmMinificationMathematicsApplied mathematicsMultivariate statisticsPerturbation (astronomy)Function approximationApproximation theory

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