(untitled) (Journal of Computational Mathematics, 2024)
In this paper, we analyze the convergence properties of a stochastic augmented Lagrangian method for solving stochastic convex programming problems with inequality constraints. Approximation models for stochastic convex programming problems are constructed from stochastic observations of real objective and constraint functions. Based on relations between solutions of the primal problem and solutions of the dual problem, it is proved that the convergence of the algorithm from the perspective of the dual problem. Without assumptions on how these random models are generated, when estimates are merely sufficiently accurate to the real objective and constraint functions with high enough, but fixed, probability, the method converges globally to the optimal solution almost surely. In addition, sufficiently accurate random models are given under different noise assumptions. We also report numerical results that show the good performance of the algorithm for different convex programming problems with several random models.