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

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.

Automated summary

This study investigates the method of approximately finding the global minimum of a positive semidefinite Hankel matrix under linear constraints, and provides a lower bound on the objective function based on conclusions from nonnegative polynomials, semi-infinite programming, and the dual theorem. It is proven that this lower bound is almost half of the number of linear constraints in the optimization problem.