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  

A dual inexact alternating direction method of multipliers for the nuclear norm regularized least squares problem

作　　者：史冰冰 王青松 SHI Bing-bing;WANG Qing-song(School of Mathematics,Southwest Jiaotong University,Chengdu 611731,China;School of Mathematical Science,Beihang University,Beijing 100191,China)

机构地区：[1]西南交通大学数学学院,四川成都611731 [2]北京航空航天大学数学科学学院,北京100191

出　　处：《高校应用数学学报（A辑）》2020年第2期181-190,共10页Applied Mathematics A Journal of Chinese Universities(Ser.A)

摘　　要：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.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.

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 

分 类 号：O242.2[理学—计算数学]