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

Yi Xu | Zendy; Xiaorong Ren | Zendy; Xihong Yan | Zendy

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

Author(s) -

Yi Xu,

Xiaorong Ren,

Xihong Yan

Publication year - 2021

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2021/2524016

Subject(s) - hankel matrix , mathematics , rank (graph theory) , semidefinite programming , upper and lower bounds , minification , combinatorics , matrix (chemical analysis) , positive definite matrix , linear programming , mathematical optimization , mathematical analysis , eigenvalues and eigenvectors , materials science , physics , quantum mechanics , composite material

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.

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