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• ε -dragging technique was introduced into BLS to improve the discriminative ability. • Regularization is adopted to optimize network structure. • Theoretical analysis verifies the convergence of the algorithm. • Numerical simulations are conducted to verify the performance of the algorithm. This paper presents the framework of the smoothing group L 1 / 2 regularized discriminative broad learning system for pattern classification and regression. The core idea is to improve the sparseness of the standard broad learning system and improve performance on recognition and generalization. First, the ε -dragging technique is introduced into the standard broad learning system to relax regression targets and enlarge distances between categories. Then, we integrate the group L 1 / 2 regularization to optimize the network architecture to achieve sparsity. For the original group L 1 / 2 regularization, the objective function is non-convex and non-smooth, which is hard for theoretical analysis. Therefore, we propose a simple and effective smoothing technique, i.e.,smoothing group L 1 / 2 regularization, which can effectively eliminate the deficiency of the original group L 1 / 2 regularization. As a result, the final weights projection matrix has a compact form and shows discriminative power capability. In addition, the alternating direction method of multipliers was adopted to optimize the algorithm. The simulation results show that the proposed algorithm has redundancy control capability and improved performance on recognition and generalization. The simulation results proves the efficiency of the theoretical analysis. [ABSTRACT FROM AUTHOR]