A Note on a Lower Bound on the Minimum Rank of a Positive Semidefinite Hankel Matrix Rank Minimization Problem-Reference-Cited by-同舟云学术

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

Published:2021-02-11 Issue: Volume:2021 Page:1-6
ISSN:1563-5147
Container-title:Mathematical Problems in Engineering
language:en
Short-container-title:Mathematical Problems in Engineering

Author:

Xu Yi¹²^ORCID,Ren Xiaorong³,Yan Xihong³

Affiliation:

1. Institute of Mathematics, Southeast University, Nanjing 210096, Jiangsu Province, China

2. Nanjing Center for Applied Mathematics, Nanjing, China

3. Department of Mathematics, Taiyuan Normal University, Jinzhong 030619, Shanxi Province, China

Abstract

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.

Funder

National Natural Science Foundation of China

Publisher

Hindawi Limited

Subject

General Engineering,General Mathematics

Link

http://downloads.hindawi.com/journals/mpe/2021/2524016.pdf

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