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We propose a sequential quadratic programming (SQP) method that canincorporate adaptive sampling for stochastic nonsmooth nonconvex optimizationproblems with upper-C^2 objectives. Upper-$\Ctwo$ functions can be viewed asdifference-of-convex (DC) functions with smooth convex parts. They are commonamong certain classes of solutions to parametric optimization problems, e.g.,recourse of stochastic programming and closest-point projection onto closedsets. Our proposed algorithm is a stochastic SQP with line search and boundedalgorithmic parameters and is shown to achieve subsequential convergence inexpectation for nonsmooth problems with upper-C^2 objectives. We discussvarious sampling strategies, including an adaptive sampling one, that canpotentially improve algorithm efficiency. The capabilities of our algorithm aredemonstrated by solving a joint production, pricing and shipment problem, aswell as a realistic optimal power flow problem as used in current power gridindustry practice.

A sequential quadratic programming method for nonsmooth stochastic optimization with upper-C^2 objective