What question did this study set out to answer?

This research aims to improve efficiency in finding roots of multivariate gradient equations under noisy conditions.

Multivariate stochastic approximation using a simultaneous perturbation gradient approximation

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Randomized trial demonstrates enhanced efficiency of a new algorithm in function minimization with noisy measurements.

This research aims to improve efficiency in finding roots of multivariate gradient equations under noisy conditions.
Developed a stochastic approximation algorithm based on simultaneous perturbation gradient approximation.
Compared performance with standard finite-difference Kiefer-Wolfowitz type procedures.
Conducted theoretical analysis and numerical simulations.
The proposed algorithm significantly outperforms standard algorithms in large-dimensional problems.
Enhanced efficiency was demonstrated through various numerical tests.

James C. Spall (1992) studied this question.

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