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A Hereditary Property of Cutting Plane Procedures — arXiv:2609.02038

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.02038
License (as archived): CC0-1.0
Archived: 2026-10-17T05:25:49.222Z
SHA-256 of the archived text: e6f9815f4e490dc61f2141e24814058ab16f2a297bb1952a76de21c7a40b650b
Stable URL of this page: https://metraipolis.com/documento/dc_ea035cfa8ca9

How to cite

A Hereditary Property of Cutting Plane Procedures — arXiv:2609.02038 — arXiv (en), https://arxiv.org/abs/2609.02038 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_ea035cfa8ca9 (Metraipolis archive dc_ea035cfa8ca9, sha256 e6f9815f4e490dc61f2141e24814058ab16f2a297bb1952a76de21c7a40b650b)

BibTeX

@misc{dcea035cfa8ca9,
  title = {A Hereditary Property of Cutting Plane Procedures — arXiv:2609.02038},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.02038},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_ea035cfa8ca9; sha256 e6f9815f4e490dc61f2141e24814058ab16f2a297bb1952a76de21c7a40b650b},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.02038. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Let $K'$ denote the closure of a convex set $K$ under a given cutting-plane procedure. The procedure satisfies the \emph{hereditary property} if $F' = K' \cap F$ for every face $F$ of $K$. The property underlies inductive proofs of finite-rank and the polyhedrality of closures, and it is an admissibility requirement in abstract frameworks for cutting-plane procedures. Yet, it has not been studied systematically across well-known cutting-plane procedures. We establish two sufficient conditions for the property. The first applies to procedures that can be expressed as closures under intersection cuts from a family of lattice-free convex sets, when a single family realizes the closure of $K$ and of each of its faces. It yields the hereditary property for the split, lift-and-project, Lovász--Schrijver, Sherali--Adams, and Lasserre closures, applied over general convex sets and for faces that need not be exposed. The second applies to procedures whose cuts are valid inequalities for Gomory's corner polyhedron, and it yields the hereditary property for the closure of Dantzig cuts derived from all bases. We complement these results with four classical procedures for which the hereditary property fails, namely the closure of Gomory's fractional cuts (derived from either all bases or feasible bases only), the mixed-integer Chvátal closure, the $+$-cut closure, and the closure of Dantzig cuts derived from feasible bases.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-03 in math.OC).
Categorie arXiv: Optimization and Control (math.OC).
Pagina del lavoro: https://arxiv.org/abs/2609.02038 — 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 2026-10-17T04:44:15.053Z dalla pagina https://arxiv.org/catchup/math.OC/2026-09-03?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).