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高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2020, Vol. 35 Issue (2): 181-190    DOI:
    
A dual inexact alternating direction method of multipliers for the nuclear norm regularized least squares problem
SHI Bing-bing, WANG Qing-song
1. School of Mathematics, Southwest Jiaotong University, Chengdu 611731;
2. School of Mathematical Science, Beihang University, Beijing 100191
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Abstract  All things in the data age can be described by data record. In data analysis, the problem
of matrix completion is to supplement some missing data. This kind of problem has been studied to a
certain extent. For instance, the desired results are achieved by solving the nuclear norm regularized
least squares problem. In this paper, starting from the duality of the problem, the alternating direction
method of multipliers (ADMM) is used to solve the problem. Under some assumptions, the global
convergence of the inexact dual ADMM (dADMM) are discussed. In the numerical experiments, by
comparing it with the primal ADMM (pADMM) to demonstrate the superiority of the algorithm.

Key words： inexact alternating direction method of multipliers      nuclear norm regularized least squares problem      dual problem      matrix completion     
Published: 07 July 2020
CLC:  O242.2  
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SHI Bing-bing
WANG Qing-song
Cite this article:

SHI Bing-bing, WANG Qing-song. A dual inexact alternating direction method of multipliers for the nuclear norm regularized least squares problem. Applied Mathematics A Journal of Chinese Universities, 2020, 35(2): 181-190.

URL:

http://www.zjujournals.com/amjcua/     OR     http://www.zjujournals.com/amjcua/Y2020/V35/I2/181


基于对偶的不精确交替方向乘子法求解核范数正则化最小二乘问题

数据时代的所有事物都可以用数据描述记录. 在数据分析中, 对部分缺失数
据补充, 即矩阵补全问题. 此类问题已有一定的研究, 如通过求解核范数正则化最小二
乘问题来达到所需效果. 该文从对偶问题出发, 使用交替方向乘子法(ADMM)来求解.
在一定假设条件下, 讨论了不精确对偶交替方向乘子法(dADMM)的全局收敛性. 数值
试验中, 通过与原问题交替方向乘子法(pADMM)进行比较, 验证了该算法的优越性.

关键词： 不精确交替方向乘子方法,  核范数正则化最小二乘问题,  对偶问题,  矩阵补 
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