• 论文 •

### 低秩稀疏矩阵恢复的快速非单调交替极小化方法

1. 工程科学计算山西省高等学校重点实验室(太原师范学院), 晋中 030619
• 收稿日期:2020-07-14 出版日期:2021-11-14 发布日期:2021-11-12
• 通讯作者: 王川龙,clwang1964@163.com
• 基金资助:
国家自然科学基金（11371275）和山西省自然科学基金（201601D011004）资助.

Sun Qingqing, Wang Chuanlong. FAST ALTERNATING MINIMIZATION METHOD WITH NON-MONOTONE SEARCH FOR LOW-RANK AND SPARSE MATRIX RECOVERY[J]. Mathematica Numerica Sinica, 2021, 43(4): 516-528.

### FAST ALTERNATING MINIMIZATION METHOD WITH NON-MONOTONE SEARCH FOR LOW-RANK AND SPARSE MATRIX RECOVERY

Sun Qingqing, Wang Chuanlong

1. Key Laboratory of Engineering and Computational Science (Taiyuan Normal University), Shanxi Province Department of Education, Jinzhong 030619, China
• Received:2020-07-14 Online:2021-11-14 Published:2021-11-12

In this paper, we propose a fast alternating minimization method with non-monotone line search technique for a non-convex optimization model of low-rank and sparse matrix recovery problem. The main idea is to use the alternating minimization method for the low-rank matrix part, and use the non-monotone line search technique for the sparse matrix part to iteratively update, respectively. The non-monotone line search technique relaxes the single-step descent into a multi-step descent, which greatly improves the computational efficiency. The paper also gives the convergence analysis of the new algorithm. Finally, the comparison of numerical experiments show that the alternate minimization method of the non-monotone technique of matrix recovery is more effective than the original monotone method.

MR(2010)主题分类:

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