仿射秩最小化问题的一种解法  

An Algorithm for Affine Rank Minimization Problem

作　　者：王展梁 刘新国[1] WANG Zhan-Liang;LIU Xin-Guo(School of Mathematical Sciences, Ocean University of China, Qingdao 266100, China)

机构地区：[1]中国海洋大学数学科学学院,山东青岛266100

出　　处：《中国海洋大学学报（自然科学版）》2021年第4期142-146,共5页Periodical of Ocean University of China

基　　金：国家自然科学基金项目(11871444,11701538)资助。

摘　　要：低秩矩阵恢复问题在众多领域有重要应用。由于秩函数的复杂性,通常寻求其替代函数进而求解松弛问题。核范数是普遍使用的替代函数之一,但其恢复能力有限。本文提出了一种新的松弛模型用于求解低秩矩阵恢复问题,并给出了邻近梯度下降算法,证明了算法的收敛性。实验数据表明模型的恢复能力远高于核范数模型。算法对于含噪声的情形同样适用,与核范数相比,仍然具有优越性。Low rank matrix restoration problem has important applications in many fields.Existing work mainly seek its substitute functions to solve the corresponding relaxation problems due to the complexity of the rank function.The nudear norm is one of the most commonly used alternative functions,but its recovery performance is limited.We propose a new relaxation model to solve low rank matrix restotration problems,develop its proximal gradient algorithm and present the convergence analysis of the algorithm.Experimental data illustrate that our method performs much better than the methods using the kernel norm.This algorithmcan bealso applicable to thenoisecase,compared with the kernel norm,it still has advantages.

关 键 词：低秩矩阵 核范数 邻近算子 松弛模型 秩函数 

分 类 号：O241.5[理学—计算数学]