2015/06/19 by Fengmin Xu, Zongben Xu, Xu, Fengmin +3
Computer Science · Engineering · #Blind Source Separation Techniques #Distributed Sensor Networks and Detection Algorithms #FOS: Mathematics #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1506.05867
openalex publication_date 2015/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recently, L1 regularization have been attracted extensive attention and successfully applied in mean-variance portfolio selection for promoting out-of-sample properties and decreasing transaction costs. However, L1 regularization approach is ineffective in promoting sparsity and selecting regularization parameter on index tracking with the budget and no-short selling constraints, since the 1-norm of the asset weights will have a constant value of one. Our recent research on L1/2 regularization has found that the half thresholding algorithm with optimal regularization parameter setting strategy is the fast solver of L1/2 regularization, which can provide the more sparse solution. In this paper we apply L1/2 regularization method to stock index tracking and establish a new sparse index tracking model. A hybrid half thresholding algorithm is proposed for solving the model. Empirical tests of model and algorithm are carried out on the eight data sets from OR-library. The optimal tracking portfolio obtained from the new model and algorithm has lower out-of-sample prediction error and consistency both in-sample and out-of-sample. Moreover, since the automatic regularization parameters are selected for the fixed number of optimal portfolio, our algorithm is a fast solver, especially for the large scale problem.