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

作　　者：胡同 

机构地区：[1]河北工业大学理学院,天津

出　　处：《应用数学进展》2024年第3期1176-1186,共11页Advances in Applied Mathematics

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。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.

关 键 词：加速ADMM 非遍历收敛速率 M-V模型 

分 类 号：TP3[自动化与计算机技术—计算机科学与技术]