A stochastic quasigradient algorithm with variable metric

This paper deals with a new variable metric algorithm for stochastic optimization problems. The essence of this is as follows: there exist two stochastic quasigradient algorithms working simultaneously — the first in the main space, the second with respect to the matrices that modify the space variables. Almost sure convergence of the algorithm is proved for the case of the convex (possiblynonsmooth) objective function.