一种求解矩阵填充问题的原始对偶加速算法  

A PRIMAL-DUAL ACCELERATION ALGORITHM FOR MATRIX COMPLETION PROBLEMS

作　　者：闫喜红[1] 张宁 段永红[2] Yan Xihong;Zhang Ning;Duan Yonghong(College of Mathematics and Statistics,Taiyuan Normal University,Jinzhong 030619;Department of Mathematics,Taiyuan University,Taiyuan 030032)

机构地区：[1]太原师范学院数学与统计学院,晋中030619 [2]太原学院数学系,太原030032

出　　处：《高等学校计算数学学报》2024年第2期121-136,共16页Numerical Mathematics A Journal of Chinese Universities

基　　金：山西省科技创新人才团队专项(202204051002018);山西省回国留学人员科研教研资助项目(2022-170)资助。

摘　　要：1引言矩阵填充在机器学习[1-2],图像处理[3]和计算机视觉[4]等领域有着广泛的应用.这些领域经常需要分析处理大规模、高维数的数据,且数据多数是以矩阵的形式储存.但是,在处理过程中这些数据经常会出现缺失现象,如何补全缺失的数据,即如何补全一个有缺失元素的矩阵,这样的问题就称为矩阵填充.低秩矩阵填充技术是一个重要的数据分析工具,其数学模型为.Matrix completion has a wide application in many areas such as machine learning,image processing,and computer vision.The primal-dual algorithm is one of the classic algorithms for solving matrix completion problems.However,when solving large-scale matrix completion problems,the efficiency of this primaldual algorithm is still needed to be further improved.Therefore,on the basis of the primal-dual algorithm framework,this paper improves the efficiency of the algorithm through the correction technique,and proposes a primal-dual acceleration algorithm by adding a correction step.Under reasonable assumptions,its global convergence is proved.Finally,numerical experiments are carried out to verify its effectiveness.

关 键 词：数学模型 原始对偶 计算机视觉 机器学习 图像处理 加速算法 处理过程 矩阵填充 

分 类 号：O221[理学—运筹学与控制论] O224[理学—数学]