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Simple Cuts, Simple Landscape: Dimension-Free Rank Bounds for Burer-Monteiro Factorizations via Rank-Width — arXiv:2610.40872

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.40872
License (as archived): CC0-1.0
Archived: 2026-11-03T05:42:35.805Z
SHA-256 of the archived text: 46d4d448a98475d198afc15ea26011b4b80477d98ee17dc62ac04e28aafd89e2
Stable URL of this page: https://metraipolis.com/documento/dc_cdf7a2c4a080

How to cite

Simple Cuts, Simple Landscape: Dimension-Free Rank Bounds for Burer-Monteiro Factorizations via Rank-Width — arXiv:2610.40872 — arXiv (en), https://arxiv.org/abs/2610.40872 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_cdf7a2c4a080 (Metraipolis archive dc_cdf7a2c4a080, sha256 46d4d448a98475d198afc15ea26011b4b80477d98ee17dc62ac04e28aafd89e2)

BibTeX

@misc{dccdf7a2c4a080,
  title = {Simple Cuts, Simple Landscape: Dimension-Free Rank Bounds for Burer-Monteiro Factorizations via Rank-Width — arXiv:2610.40872},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.40872},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_cdf7a2c4a080; sha256 46d4d448a98475d198afc15ea26011b4b80477d98ee17dc62ac04e28aafd89e2},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.40872. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In this work, we study Burer-Monteiro factorizations of semidefinite programs with unit diagonal constraints. For a real symmetric cost matrix whose rank-width over $\mathbb{R}$ is at most $k$, we prove that every non-flat second-order stationary point of the factorized problem is globally optimal whenever the factorization rank is at least $2k$, independently of the matrix size.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.OC, nuovi lavori del giorno).
Categorie arXiv: Optimization and Control (math.OC).
Pagina del lavoro: https://arxiv.org/abs/2610.40872 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-03T05:31:17.147Z dalla pagina https://arxiv.org/list/math.OC/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).