  We propose a sequential quadratic programming (SQP) method that can
incorporate adaptive sampling for stochastic nonsmooth nonconvex optimization
problems with upper-C^2 objectives. Upper-$\Ctwo$ functions can be viewed as
difference-of-convex (DC) functions with smooth convex parts. They are common
among certain classes of solutions to parametric optimization problems, e.g.,
recourse of stochastic programming and closest-point projection onto closed
sets. Our proposed algorithm is a stochastic SQP with line search and bounded
algorithmic parameters and is shown to achieve subsequential convergence in
expectation for nonsmooth problems with upper-C^2 objectives. We discuss
various sampling strategies, including an adaptive sampling one, that can
potentially improve algorithm efficiency. The capabilities of our algorithm are
demonstrated by solving a joint production, pricing and shipment problem, as
well as a realistic optimal power flow problem as used in current power grid
industry practice.
