Fabian's algorithm in the theory of self-adjusting systems (Q1058502)

The convergence of Fabian's modification [see \textit{V. Fabian}, Czechosl. Math. J. 10(85), 123-159 (1960; Zbl 0127.102)] of the Robbins-Monro and Kiefer-Wolfowitz stochastic approximation algorithms is studied in the case of a nonunique solution. It is shown that under conditions natural for such situation, these algorithms will converge with positive probability from any initial approximation to isolated stable points of the set of solutions.