A stochastic programming problem in which the optimum is sought with respect to the mathematical expectation is considered in the paper. Moreover, it is assumed that the objective function is nondifferentiable.
The aim of the paper is to present a new recursive stochastic subgradient method. In this method successive directions are obtained from quadratic programming subproblems and further, the idea of averaging stochastic subgradients along trajectory by a filter is used. A special Lyapunov function technique is applied to prove the convergence properties.