低秩稀疏矩阵恢复的快速非单调交替极小化方法  

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

作　　者：孙青青 王川龙[1] Sun Qingqing;Wang Chuanlong(Key Laboratory of Engineering and Computational Science(Taiyuan Normal University),Shanxi Province Department of Education,Jinzhong 030619,China)

机构地区：[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

出　　处：《计算数学》2021年第4期516-528,共13页Mathematica Numerica Sinica

基　　金：国家自然科学基金(11371275);山西省自然科学基金(201601D011004)资助。

摘　　要：针对低秩稀疏矩阵恢复问题的一个非凸优化模型,本文提出了一种快速非单调交替极小化方法.主要思想是对低秩矩阵部分采用交替极小化方法,对稀疏矩阵部分采用非单调线搜索技术来分别进行迭代更新.非单调线搜索技术是将单步下降放宽为多步下降,从而提高了计算效率.文中还给出了新算法的收敛性分析.最后,通过数值实验的比较表明,矩阵恢复的非单调交替极小化方法比原单调类方法更有效.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.

关 键 词：矩阵恢复 交替极小化 低秩稀疏矩阵 非单调线搜索 

分 类 号：O224[理学—运筹学与控制论]