.png){kind=icon}
返回
Rank-constrained optimization and its applications
.png){kind=icon}
OA
AI
DOI：10.1016/j.automatica.2017.04.039.png)
.png){kind=icon}
.png){kind=icon}
分享.png){kind=icon}
收藏
摘要
En 中文
This paper investigates an iterative approach to solve the general rank-constrained optimization problems (RCOPs) defined to optimize a convex objective function subject to a set of convex constraints and rank constraints on unknown rectangular matrices. In addition, rank minimization problems (RMPs) are introduced and equivalently transformed into RCOPs by introducing a quadratic matrix equality constraint. The rank function is discontinuous and nonconvex, thus the general RCOPs are classified as NP-hard in most of the cases. An iterative rank minimization (IRM) method, with convex formulation at each iteration, is proposed to gradually approach the constrained rank. The proposed IRM method aims at solving RCOPs with rank inequalities constrained by upper or lower bounds, as well as rank equality constraints. Proof of the convergence to a local minimizer with at least a sublinear convergence rate is provided. Four representative applications of RCOPs and RMPs, including system identification, output feedback stabilization, and structured H-2 controller design problems, are presented with comparative simulation results to verify the feasibility and improved performance of the proposed IRM method. (C) 2017 Elsevier Ltd. All rights reserved.
Keyword:
Rank-constrained optimization
Matrix rank minimization
Convex relaxation
Semidefinite programming
Feedback control
AI总结
对已上传原文的论文进行重点信息的提取，主要内容包括：简要概述、研究摘要、背景介绍、关键亮点、图文解析、展望与总结。
期刊
IF:
5.9
论文数:
1.2W
被引数:
5.2W
机构
引用论文
On the rank minimization problem over a positive semidefinite linear matrix inequality关于半正定线性矩阵不等式的秩最小化问题
PREAI
分享收藏Low-order control design for LMI problems using alternating projection methods使用交替投影方法的LMI问题的低阶控制设计.png)
AUTOMATICA
AUTOMATICAIF5.9
PREAI
分享收藏分享收藏
查看更多内容