An efficient method for solving a matrix least squares problem over a matrix inequality constraint

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• 作者：Jiao-fen Li ; Wen Li ; Ru Huang
• 关键词：Matrix inequality ; Least squares problem ; Matrix equation ; Alternating direction method ; Iteration method ; 15A24 ; 15A57 ; 65F10 ; 65F30
• 刊名：Computational Optimization and Applications
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：63
• 期：2
• 页码：393-423
• 全文大小：1,625 KB
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• 作者单位：Jiao-fen Li (1) (2)
  Wen Li (1)
  Ru Huang (3)
  
  1. School of Mathematical Sciences, South China Normal University, Guangzhou, People’s Republic of China
  2. School of Mathematics and Computing Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guilin, People’s Republic of China
  3. School of Mathematical Sciences, Fudan University, Shanghai, People’s Republic of China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Optimization
  Operations Research and Mathematical Programming
  Operation Research and Decision Theory
  Statistics
  Convex and Discrete Geometry
  
• 出版者：Springer Netherlands
• ISSN：1573-2894

文摘

In this paper, we consider solving a class of matrix inequality constrained matrix least squares problems of the form $$\begin{aligned} \begin{array}{rl} \text {min}&{}\dfrac{1}{2}\Vert \sum \limits _{i=1}^{t}A_iXB_i-C\Vert^2\\ \text {subject}\ \text {to}&{} L \le EXF\le U, \ \ X\in \mathcal {S}, \end{array} \end{aligned}$$