Convergence analysis of projected gradient descent for Schatten-p nonconvex matrix recovery

The matrix rank minimization problem arises in many engineering applications. As this problem is NP-hard, a nonconvex relaxation of matrix rank minimization, called the Schatten-p quasi-norm minimization（0 〈 p 〈 1）, has been developed to approximate the rank function closely. We study the performanc...

Full description

Saved in:
Bibliographic Details
Published in:Science China. Mathematics 2015-04, Vol.58 (4), p.845-858
Main Authors: Cai, Yun, Li, Song
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematics
Mathematics and Statistics
rank函数
投射
指数收敛速度
收敛性分析
最小化问题
梯度下降算法
矩阵秩
非凸
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The matrix rank minimization problem arises in many engineering applications. As this problem is NP-hard, a nonconvex relaxation of matrix rank minimization, called the Schatten-p quasi-norm minimization（0 〈 p 〈 1）, has been developed to approximate the rank function closely. We study the performance of projected gradient descent algorithm for solving the Schatten-p quasi-norm minimization（0 〈 p 〈 1） problem.Based on the matrix restricted isometry property（M-RIP）, we give the convergence guarantee and error bound for this algorithm and show that the algorithm is robust to noise with an exponential convergence rate.
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-014-4949-1