Autonomous sparse Markowitz portfolio based on two-stage accelerated forward-backward algorithm

作     者：Lin, Yizun Wang, Linhui Lai, Zhao-Rong 

作者机构：Jinan Univ Coll Informat Sci & Technol Dept Math Guangzhou 510632 Peoples R China Beijing Normal Univ Sch Stat Beijing 100875 Peoples R China 

出 版 物：《EXPERT SYSTEMS WITH APPLICATIONS》 (Expert Sys Appl)

年 卷 期：2025年第271卷

核心收录：

学科分类：1201[管理学-管理科学与工程(可授管理学、工学学位)] 0808[工学-电气工程] 08[工学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：National Natural Science Foundation of China [12401120, 62176103, 62172188] Guangdong Basic and Applied Basic Research Foundation [2021A1515110541, 2024A1515010272] Science and Technology Planning Project of Guangzhou [2024A04J3940, 2024A04J9896] 

主　　题：Markowitz portfolio l0constraint Accelerated forward-backward algorithm Local optimum 

摘      要：It is desirable but nontrivial to obtain a portfolio that enjoys both sparsity and optimality. We propose a portfolio model that is rooted in the mean-variance framework, incorporating the 80 constraint as a precise restriction to ensure a sparse portfolio comprising no more than a specified number of assets. Moreover, the simplex constraint is also imposed to ensure the feasibility of portfolio. This model is difficult to solve due to the nonconvexity of the 80 constraint and the geometric complexity of the intersection of the two constraints. To address this issue, we establish the equivalence relation between a local optimum of a general 80-constrained problem and a global optimum on a restricted set of variables. Based on this result, we develop a two-stage accelerated forward-backward algorithm that converges to a locally optimal solution to the proposed autonomous sparse Markowitz portfolio model, with an o(1/k2) convergence rate in terms of function value. Extensive experiments on 7 benchmark data sets from real-world financial markets show that the proposed method achieves state-of-the-art performance in various evaluating metrics.