A Note on a Lower Bound on the Minimum Rank of a Positive Semidefinite Hankel Matrix Rank Minimization Problem

被引：0

作者：

Xu, Yi ^{[1
,2
]}

Ren, Xiaorong ^{[3
]}

Yan, Xihong ^{[3
]}

机构：

[1] Southeast Univ, Inst Math, Nanjing 210096, Jiangsu, Peoples R China

[2] Nanjing Ctr Appl Math, Nanjing, Peoples R China

[3] Taiyuan Normal Univ, Dept Math, Jinzhong 030619, Shanxi, Peoples R China

来源：

MATHEMATICAL PROBLEMS IN ENGINEERING | 2021年 / 2021卷

基金：

中国国家自然科学基金;

关键词：

D O I：

10.1155/2021/2524016

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

This paper investigates the problem of approximating the global minimum of a positive semidefinite Hankel matrix minimization problem with linear constraints. We provide a lower bound on the objective of minimizing the rank of the Hankel matrix in the problem based on conclusions from nonnegative polynomials, semi-infinite programming, and the dual theorem. We prove that the lower bound is almost half of the number of linear constraints of the optimization problem.

引用

页数：6

共 50 条

[1] A new lower bound for the positive semidefinite minimum rank of a graph
Zimmer, Andrew M.
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2013, 438 (03) : 1095 - 1112
[2] A NOTE ON THE POSITIVE SEMIDEFINITE MINIMUM RANK OF A SIGN PATTERN MATRIX
Cai, Xinzhong
Wang, Xinmao
[J]. ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 2013, 26 : 345 - 356
[3] On the rank minimization problem over a positive semidefinite linear matrix inequality
Mesbahi, M
Papavassilopoulos, GP
[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1997, 42 (02) : 239 - 243
[4] A Lower Bound on the Positive Semidefinite Rank of Convex Bodies
Fawzi, Hamza
El Din, Mohab Safey
[J]. SIAM JOURNAL ON APPLIED ALGEBRA AND GEOMETRY, 2018, 2 (01): : 126 - 139
[5] Minimum rank positive semidefinite solution to the matrix approximation problem in the spectral norm
Liu, Xifu
Luo, Le
[J]. APPLIED MATHEMATICS LETTERS, 2020, 107
[6] Polytopes of Minimum Positive Semidefinite Rank
João Gouveia
Richard Z. Robinson
Rekha R. Thomas
[J]. Discrete & Computational Geometry, 2013, 50 : 679 - 699
[7] Polytopes of Minimum Positive Semidefinite Rank
Gouveia, Joao
Robinson, Richard Z.
Thomas, Rekha R.
[J]. DISCRETE & COMPUTATIONAL GEOMETRY, 2013, 50 (03) : 679 - 699
[8] A lower bound for minimum positive semidefinite rank by constructing an OS-vertex set for a given graph
Lei, Li
Huang, Ting-Zhu
[J]. INFORMATION-AN INTERNATIONAL INTERDISCIPLINARY JOURNAL, 2011, 14 (06): : 1873 - 1878
[9] Unitary matrix digraphs and minimum semidefinite rank
Jiang, Yunjiang
Mitchell, Lon H.
Narayan, Sivaram K.
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2008, 428 (07) : 1685 - 1695
[10] Positive Semidefinite Matrix Factorization: A Connection With Phase Retrieval and Affine Rank Minimization
Lahat, Dana
Lang, Yanbin
Tan, Vincent Y. F.
Fevotte, Cedric
[J]. IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2021, 69 : 3059 - 3074

← 1 2 3 4 5 →