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PreprintCC BY 4.0arXiv

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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Cite

BibTeXRIS
BibTeX
@misc{zeiss2026comment,
  title = {{Comment on "The polarization hierarchy for polynomial optimization over convex bodies, with applications to nonnegative matrix rank"}},
  author = {Julius A. Zeiss},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.24542},
  eprint = {2610.24542},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.24542},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Comment on "The polarization hierarchy for polynomial optimization over convex bodies, with applications to nonnegative matrix rank"
AU  - Julius A. Zeiss
PY  - 2026
DA  - 2026/10/17
PB  - arXiv
DO  - 10.48550/arxiv.2610.24542
UR  - https://arxiv.org/abs/2610.24542
AB  - 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.
ER  -