南京师大学报（自然科学版）2026，Vol.49Issue(3)：1-9,9.DOI:10.3969/j.issn.1001-4616.2026.03.001
一种求解低秩矩阵最小化问题的非凸分式模型的对称ADMM算法研究
Research on a Symmetric ADMM Algorithm for Solving Nonconvex Fractional Model of Low Rank Matrix Minimization Problems
摘要
Abstract
Due to the nonconvex and discontinuous properties of the low rank matrix minimization problem,this paper considers a nonconvex fractional model that approximates the rank function.By exploiting the separability structure of the nonconvex fractional model,a symmetric ADMM algorithm is developed to solve this model.Compared to traditional ADMM,this method incorporates a relaxation coefficient α into the multiplier update term Λk+1/2,which allows to speed up the convergence of the algorithm.Under suitable assumptions,the subsequential and global convergence of the new algorithm are established.Finally,numerical experiments are performed to verify the effectiveness of the proposed method.关键词
非凸分式模型/对称ADMM/收敛性Key words
nonconvex fractional model/symmetric ADMM/convergence分类
数理科学引用本文复制引用
张思宇,张欣,沈博涛,葛志利..一种求解低秩矩阵最小化问题的非凸分式模型的对称ADMM算法研究[J].南京师大学报（自然科学版）,2026,49(3):1-9,9.基金项目
国家自然科学基金资助项目(120081、12471290)、江苏省青蓝工程和大规模复杂系统数值模拟教育部重点实验室开放课题基金资助项目. （120081、12471290）
