  The paper deals with stochastic difference-of-convex functions (DC) programs,
that is, optimization problems whose the cost function is a sum of a lower
semicontinuous DC function and the expectation of a stochastic DC function with
respect to a probability distribution. This class of nonsmooth and nonconvex
stochastic optimization problems plays a central role in many practical
applications. Although there are many contributions in the context of convex
and/or smooth stochastic optimization, algorithms dealing with nonconvex and
nonsmooth programs remain rare. In deterministic optimization literature, the
DC Algorithm (DCA) is recognized to be one of the few algorithms to solve
effectively nonconvex and nonsmooth optimization problems. The main purpose of
this paper is to present some new stochastic DCAs for solving stochastic DC
programs. The convergence analysis of the proposed algorithms is carefully
studied, and numerical experiments are conducted to justify the algorithms'
behaviors.
