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In this paper application of the stochastic approximation algorithm with randomized differences to the minimum tracking problem for the non-constrained optimization is considered. The upper bound of mean-squared estimation error is derived in the case of once differentiable functional and almost arbitrary observation noise. Numerical simulation of the estimates stabilization for the multidimensional optimization with unknown but bounded deterministic noise is provided. Stabilization bound has sufficiently small level comparing to significant level of noise.