New bounds for the integer Caratheodory rank

Aliev, Iskander ORCID: https://orcid.org/0000-0002-2206-9207, Henk, Martin, Hogan, Mark, Kuhlmann, Stefan and Oertel, Timm 2024. New bounds for the integer Caratheodory rank. SIAM Journal on Optimization 34 (1) , pp. 190-200. 10.1137/23M1561312

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Abstract

Given a rational pointed n-dimensional cone C, we study the integer Caratheodory rank CR(C) and its asymptotic form CR^a(C), where we consider “most” integer vectors in the cone. The main result significantly improves the previously known upper bound for CR^a(C). We also study bounds on CR(C) in terms of ∆, the maximal absolute n × n minor of the matrix given in an integral polyhedral representation of C. If ∆ ∈ {1,2}, we show CR(C) = n, and prove upper bounds for simplicial cones, improving the best known upper bound on CR(C) for ∆ ≤ n.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Schools > Mathematics
Publisher:	Society for Industrial and Applied Mathematics
ISSN:	1052-6234
Date of First Compliant Deposit:	27 September 2023
Date of Acceptance:	24 September 2023
Last Modified:	11 Nov 2024 17:30
URI:	https://orca.cardiff.ac.uk/id/eprint/162775

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