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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2026, Vol. 42 ›› Issue (6): 991-1004.doi: 10.3969/j.issn.1005-3085.2025.06.001cstr: 32411.14.cjem.CN61-1269/O1.2025.06.001

• •    下一篇

一种改进的低秩矩阵补全加速近端梯度法

闫喜红,   兰   泽,   逯婧瑜   

  1. 太原师范学院数学与统计学院智能优化计算与区块链技术山西省重点实验室，晋中  030619
  • 收稿日期:2024-10-18 接受日期:2025-06-11 出版日期:2025-12-15 发布日期:2026-02-15
  • 基金资助:
    国家自然科学基金 (12371381)；山西省科技创新人才团队专项 (202204051002018)；山西省回国留学人员科研教研项目 (2022-170).

An Improved Accelerate Proximal Gradient for Low-rank Matrix Completion

YAN Xihong,   LAN Ze,    LU Jingyu   

  1. School of Mathematics and Statistics, Shanxi Key Laboratory for Intelligent Optimization Computing and Blockchain Technology, Taiyuan Normal University, Jinzhong 030619
  • Received:2024-10-18 Accepted:2025-06-11 Online:2025-12-15 Published:2026-02-15
  • Supported by:
    The National Natural Science Foundation of China (12371381); the Science and Technology Innovation Teams of Shanxi Province (202204051002018); the Research and Teaching Research Funding Project for Returned Students in Shanxi Province (2022-170).

摘要：

针对低秩矩阵补全问题，提出了一种变步长加速近端梯度算法。该算法基于Armijo准则选取自适应变步长以实现加速，并确保目标函数在每一步迭代中单调下降，从而显著提高了计算效率。在特定假设条件下，对算法的收敛性进行了理论分析与证明。通过数值实验，进一步验证了所提出算法的有效性。

关键词: 低秩矩阵补全, 加速近端梯度算法, Armijo准则

Abstract:

This paper proposes a variable step-size accelerated proximal gradient algorithm for low-rank matrix completion. The method employs an adaptive step-size selection strategy based on the Armijo rule, which ensures a monotonic decrease of the objective function per iteration and enhances computational efficiency. The convergence of the algorithm is rigorously established under standard assumptions. Numerical experiments demonstrate the algorithm's superiority over existing methods in terms of both convergence speed and overall efficacy.

Key words: low-rank matrix completion, accelerated proximal gradient, Armijo criterion

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