Half thresholding eigenvalue algorithm for semidefinite matrix completion

The semidefinite matrix completion（SMC） problem is to recover a low-rank positive semidefinite matrix from a small subset of its entries. It is well known but NP-hard in general. We first show that under some cases, SMC problem and S1/2relaxation model share a unique solution. Then we prove that the...

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Published in:Science China. Mathematics Vol. 58; no. 9; pp. 2015 - 2032
Main Authors: Chen, YongQiang, Luo, ZiYan, Xiu, NaiHua
Format: Journal Article
Language:English
Published: Beijing Science China Press 01.09.2015
Subjects:
Algorithms
Applications of Mathematics
Convergence
Eigenvalues
Iterative methods
Mathematical models
Mathematics
Mathematics and Statistics
Optimization
Regularization
Robustness
全局最优解
半正定矩阵
参赛作品
对称矩阵
收敛性分析
特征值
算法
阈值
semidefinite matrix completion
convergence
relaxation
90C06
half thresholding eigenvalue algorithm
90C26
90C59
ISSN:1674-7283, 1869-1862
Online Access:Get full text
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Summary:The semidefinite matrix completion（SMC） problem is to recover a low-rank positive semidefinite matrix from a small subset of its entries. It is well known but NP-hard in general. We first show that under some cases, SMC problem and S1/2relaxation model share a unique solution. Then we prove that the global optimal solutions of S1/2regularization model are fixed points of a symmetric matrix half thresholding operator. We give an iterative scheme for solving S1/2regularization model and state convergence analysis of the iterative sequence.Through the optimal regularization parameter setting together with truncation techniques, we develop an HTE algorithm for S1/2regularization model, and numerical experiments confirm the efficiency and robustness of the proposed algorithm.
Bibliography:semidefinite matrix completion;S1/2relaxation;half thresholding eigenvalue algorithm;conver-gence
11-5837/O1
The semidefinite matrix completion（SMC） problem is to recover a low-rank positive semidefinite matrix from a small subset of its entries. It is well known but NP-hard in general. We first show that under some cases, SMC problem and S1/2relaxation model share a unique solution. Then we prove that the global optimal solutions of S1/2regularization model are fixed points of a symmetric matrix half thresholding operator. We give an iterative scheme for solving S1/2regularization model and state convergence analysis of the iterative sequence.Through the optimal regularization parameter setting together with truncation techniques, we develop an HTE algorithm for S1/2regularization model, and numerical experiments confirm the efficiency and robustness of the proposed algorithm.
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-015-5052-y