On multi-step procedures of stochastic optimization

The paper is concerned with multi-step procedures for function minimization to be used in the presence of random noise. Using the tools of theory of large deflections for random process the necessary and sufficient convergence conditions are derived for some procedures. The notion of a quasipotential is introduced which acts as a Lyapunov function for such procedures and asymptotic equivalence is proved for single- and twostep procedures with respect to the quasipotential. Asymptotic equivalence of these procedures in the weak sense is also studied.