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.

25 pages, Comment on this https URL (arXiv:2406.09506)

Optimization and Control (math.OC); Quantum Physics (quant-ph)

arXiv:2610.24542 [math.OC]

(or arXiv:2610.24542v1 [math.OC] for this version)

https://doi.org/10.48550/arXiv.2610.24542 Focus to learn more arXiv-issued DOI via DataCite

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