Comment on "The polarization hierarchy for polynomial optimization over convex bodies, with applications to nonnegative matrix rank"
math.OC, quant-ph
Submitted: 2026-10-17
Updated: 2026-10-17
Comments: 25 pages, Comment on https://doi.org/10.1016/j.laa.2025.05.019 (arXiv:2406.09506)
License: http://creativecommons.org/licenses/by/4.0/
The gist: We revisit the feasibility and convergence claims for the polarization hierarchy of Plávala, Ligthart and Gross [Linear Algebra Appl.
Terminology
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.
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