Scholarlink

<p>This paper considers the optimization problem of sparse and low-rank matrix recovery, which involves a least squares problem with a rank constraint and a cardinality constraint. To address the challenges posed by these constraints, an asymptotic difference-of-convex (ADC) method is proposed, which employs a Moreau smoothing approach and an exact penalty approach to gradually transform this problem into a DC programming format. To solve the resulting DC programming problem, an efficient inexact DC algorithm with sieving strategy (siDCA) is introduced, which fully utilizes the DC structure. The subproblems of siDCA are efficiently solved using a dual-based semismooth Newton method. The convergence of the solution sequence generated by siDCA is proved. To demonstrate the effectiveness of the proposed ADC-siDCA method, matrix recovery experiments on nonnegative and positive semidefinite matrices are conducted. Numerical results are compared with those obtained using successive DC approximation minimization method and penalty proximal alternating linearized minimization approach, respectively. The comparison indicates that ADC-siDCA outperforms the other two methods in terms of efficiency and recovery error. Additionally, numerical experiments on sparse phase retrieval illustrate that ADC-siDCA is valuable for recovering sparse and low-rank Hermitian matrices.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

An Efficient Asymptotic DC Method for Sparse and Low-Rank Matrix Recovery

  • 期刊论文

  • 发表日期：

    2025年6月11日

查看全文
  • Mingcai Ding,
  • Xiaoliang Song,
  • Bo Yu

摘要

This paper considers the optimization problem of sparse and low-rank matrix recovery, which involves a least squares problem with a rank constraint and a cardinality constraint. To address the challenges posed by these constraints, an asymptotic difference-of-convex (ADC) method is proposed, which employs a Moreau smoothing approach and an exact penalty approach to gradually transform this problem into a DC programming format. To solve the resulting DC programming problem, an efficient inexact DC algorithm with sieving strategy (siDCA) is introduced, which fully utilizes the DC structure. The subproblems of siDCA are efficiently solved using a dual-based semismooth Newton method. The convergence of the solution sequence generated by siDCA is proved. To demonstrate the effectiveness of the proposed ADC-siDCA method, matrix recovery experiments on nonnegative and positive semidefinite matrices are conducted. Numerical results are compared with those obtained using successive DC approximation minimization method and penalty proximal alternating linearized minimization approach, respectively. The comparison indicates that ADC-siDCA outperforms the other two methods in terms of efficiency and recovery error. Additionally, numerical experiments on sparse phase retrieval illustrate that ADC-siDCA is valuable for recovering sparse and low-rank Hermitian matrices.