A Note on a Lower Bound on the Minimum Rank of a Positive Semidefinite Hankel Matrix Rank Minimization Problem. (11th February 2021)

• Record Type: Journal Article
• Authors: Xu, Yi; Ren, Xiaorong; Yan, Xihong
• Other Names: Chen He Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2021(2021)
• Publication Date: 2021-02-11
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2021/2524016
• Languages: English
• ISSNs: 1024-123X

Abstract

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.