  Stochastic nonconvex optimization problems with nonlinear constraints have a
broad range of applications in intelligent transportation, cyber-security, and
smart grids. In this paper, first, we propose an inexact-proximal accelerated
gradient method to solve a nonconvex stochastic composite optimization problem
where the objective is the sum of smooth and nonsmooth functions and the
solution to the proximal map of the nonsmooth part is calculated inexactly at
each iteration. We demonstrate an asymptotic sublinear rate of convergence for
stochastic settings using increasing sample-size considering the error in the
proximal operator diminishes at an appropriate rate. Then we customize the
proposed method for solving stochastic nonconvex optimization problems with
nonlinear constraints and demonstrate a convergence rate guarantee. Numerical
results suggest that the proposed scheme compares well with competitive
methods.
