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

Yi Xu, Xiaorong Ren and Xihong Yan

Mathematical Problems in Engineering, 2021, vol. 2021, 1-6

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.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:2524016

DOI: 10.1155/2021/2524016

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