Shi Zhang-Lei, Li Xiao Peng, Leung Chi-Sing, So Hing Cheung
IEEE Trans Neural Netw Learn Syst. 2024 Feb;35(2):2901-2909. doi: 10.1109/TNNLS.2022.3192065. Epub 2024 Feb 5.
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 ( l -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.
受稀疏学习的启发，带有稀疏正则化项的马科维茨均值 - 方差模型在稀疏投资组合优化中被广泛使用。然而，在基于惩罚的投资组合优化算法中，所得投资组合的基数水平依赖于正则化参数的选择。本简报将均值 - 方差模型表述为一个基数（l - 范数）约束的非凸优化问题，在该问题中我们可以明确指定投资组合中的资产数量。然后，我们使用乘子交替方向法（ADMMs）的概念来开发一种算法以求解该约束非凸问题。与一些现有算法不同，所提出的算法可以明确控制投资组合的基数。此外，还推导了所提出算法的动态行为。在四个真实世界数据集上的数值结果证明了我们的方法相对于几种先进算法的优越性。
