Comment on "The polarization hierarchy for polynomial optimization over convex bodies, with applications to nonnegative matrix rank"

Abstract

We revisit the feasibility and convergence claims for the polarization hierarchy of Plávala, Ligthart and Gross [Linear Algebra Appl.\ 723 (2025) 15--32]. Counterexamples show that the stated assumption is insufficient for the feasibility characterization and for convergence of the hierarchy with the polarization constraint. We establish corrected results under a stronger algebraic condition and supply a missing compactness argument.

arXiv comment25 pages, Comment on https://doi.org/10.1016/j.laa.2025.05.019 (arXiv:2406.09506)