Cardinality Constrained Portfolio Optimization via Alternating Direction Method of Multipliers

• Published in: IEEE transaction on neural networks and learning systems Vol. 35; no. 2; pp. 2901 - 2909
• Main Authors: Shi, Zhang-Lei, Li, Xiao Peng, Leung, Chi-Sing, So, Hing Cheung
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.02.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; alternating direction method of multipliers (ADMMs); Convex functions; Covariance matrices; Heuristic algorithms; Indexes; mean-variance model; Multipliers; Neural networks; Optimization; Portfolios; Regularization; sparse portfolio; ℓ₀-norm
• ISSN: 2162-237X; 2162-2388; 2162-2388
• DOI: 10.1109/TNNLS.2022.3192065

Inspired by sparse learning, the Markowitz mean-variance model with a sparse regularization term is popularly used in sparse portfolio optimization. However, in penalty-based portfolio optimization algorithms, the cardinality level of the resultant portfolio relies on the choice of the regularization parameter. This brief formulates the mean-variance model as a cardinality (<inline-formula> <tex-math notation="LaTeX">\ell _{0} </tex-math></inline-formula>-norm) constrained nonconvex optimization problem, in which we can explicitly specify the number of assets in the portfolio. We then use the alternating direction method of multipliers (ADMMs) concept to develop an algorithm to solve the constrained nonconvex problem. Unlike some existing algorithms, the proposed algorithm can explicitly control the portfolio cardinality. In addition, the dynamic behavior of the proposed algorithm is derived. Numerical results on four real-world datasets demonstrate the superiority of our approach over several state-of-the-art algorithms.