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：

Compendex;

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

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