  Chance-constrained programs (CCPs) constitute a difficult class of stochastic
programs due to its possible nondifferentiability and nonconvexity even with
simple linear random functionals. Existing approaches for solving the CCPs
mainly deal with convex random functionals within the probability function. In
the present paper, we consider two generalizations of the class of chance
constraints commonly studied in the literature; one generalization involves
probabilities of disjunctive nonconvex functional events and the other
generalization involves mixed-signed affine combinations of the resulting
probabilities; together, we coin the term affine chance constraint (ACC) system
for these generalized chance constraints. Our proposed treatment of such an ACC
system involves the fusion of several individually known ideas: (a)
parameterized upper and lower approximations of the indicator function in the
expectation formulation of probability; (b) external (i.e., fixed) versus
internal (i.e., sequential) sampling-based approximation of the expectation
operator; (c) constraint penalization as relaxations of feasibility; and (d)
convexification of nonconvexity and nondifferentiability via surrogation. The
integration of these techniques for solving the affine chance-constrained
stochastic program (ACC-SP) with various degrees of practicality and
computational efforts is the main contribution of this paper.
