Sample-Based Neural Approximation Approach for Probabilistic Constrained Programs

This article introduces a neural approximation-based method for solving continuous optimization problems with probabilistic constraints. After reformulating the probabilistic constraints as the quantile function, a sample-based neural network model is used to approximate the quantile function. The statistical guarantees of the neural approximation are discussed by showing the convergence and feasibility analysis. Then, by introducing the neural approximation, a simulated annealing-based algorithm is revised to solve the probabilistic constrained programs. An interval predictor model (IPM) of wind power is investigated to validate the proposed method.