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arXiv · 2610.24542

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

Julius A. Zeiss
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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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Julius A. Zeiss. 2026-10-17. Comment on "The polarization hierarchy for polynomial optimization over convex bodies, with applications to nonnegative matrix rank". https://arxiv.org/abs/2610.24542

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