一类加速ADMM算法在投资组合选择中的应用研究

Research on the Application of a Class of Accelerated ADMM Algorithms in Portfolio Selection

摘要: Mean-Variance模型为现代投资组合选取奠定了基础。 近年来，随着金融资产数量的提高，求 解M-V模型的经典算法效率逐渐变低。 因此，有关学者提出了资产分割的ADMM算法(AS- ADMM)以提升ADMM 算法的效率。 该算法能够比经典的算法更高效，但在一些超高维的情况 下，AS-ADMM也不足以显著提高求解效率。 为了解决这个问题，本文应用外推思想，提出了部 分加速的资产分割算法(PA-AS-ADMM)，并证明了该算法的非遍历收敛速率为O( )，最后在数值实验中验证了PA-AS-ADMM的有效性。

Abstract: The Mean-Variance model laid the foundation for modern portfolio selection. In re- cent years, as the number of financial assets has increased, the efficiency of classic algorithms for solving the M-V model has gradually decreased. Therefore, scholars have proposed Asset-Splitting ADMM algorithm (AS-ADMM) to improve the efficien- cy of ADMM algorithm. This algorithm can be more efficient than the classic ones, but in high-dimensional cases, AS-ADMM is not sufficiently effective. To address this problem, this paper applies the extrapolation idea and proposes Partially Accelerated Asset Segmentation algorithm (PA-AS-ADMM), and proves that the non-ergodic con- vergence rate of this algorithm is O(). Finally, the effectiveness of PA-AS-ADMM is verified in numerical experiments.