2025/03/08 by Xu, Xin
#90C20 #90C25 #FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2503.06185
The mean-variance (MV) model is the core of modern portfolio theory. Nevertheless, it suffers from the over-fitting problem due to the estimation errors of model parameters. We consider the ℓ1 regularized MV model, which adds an ℓ1 regularization term in the objective to prevent over-fitting and promote sparsity of solutions. By investigating the relationship between sample size and over-fitting, we propose an initial regularization parameter scheme in the ℓ1 regularized MV model. Then we propose an adaptive parameter tuning strategy to control the amount of short sales. ADMM is a well established algorithm whose performance is affected by the penalty parameter. In this paper, a penalty parameter scheme based on regularized Barzilai-Borwein step size is proposed, and the modified ADMM is used to solve the ℓ1 regularized MV problem. Numerical results verify the effectiveness of the two types of parameters proposed in this paper.