  Chance constrained programming (CCP) refers to a type of optimization problem
with uncertain constraints that are satisfied with at least a prescribed
probability level. In this work, we study the sample average approximation
(SAA) of chance constraints. This is an important approach to solving CCP,
especially in the data-driven setting where only a sample of multiple
realizations of the random vector in the chance constraints is available. The
SAA is obtained by replacing the underlying distribution with an empirical
distribution over the available sample. Assuming that the functions in chance
constraints are all convex, we reformulate the SAA of chance constraints into a
difference-of-convex (DC) form. Moreover, considering that the objective
function is a difference-of-convex function, the resulting formulation becomes
a DC constrained DC program. Then, we propose a proximal DC algorithm for
solving this reformulation. In particular, we show that the subproblems of the
proximal DC are suitable for off-the-shelf solvers in some scenarios. Moreover,
we not only prove the subsequential and sequential convergence of the proposed
algorithm but also derive the iteration complexity for finding an approximate
Karush-Kuhn-Tucker point. To support and complement our theoretical
development, we show via numerical experiments that our proposed approach is
competitive with a host of existing approaches.
