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On pairs of complementary GJ pivoting transforming skew-symmetric matrices
[Submitted on 25 Oct 2024 (v1), last revised 16 Jun 2026 (this v · 2026-06-17 · via math updates on arXiv.org

Mathematics > Optimization and Control

arXiv:2410.19350 (math)

[Submitted on 25 Oct 2024 (v1), last revised 16 Jun 2026 (this version, v3)]

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Abstract:This article describes certain ratios that attend pairs of complementary Gauss-Jordan pivotings transforming skew-symmetric matrices. Our interest in those ratios was motivated by a need to prove a crucial Claim stated in a recently proposed strongly polynomial-time algorithm for the general LP problem. That Claim is proved in this article and, as a consequence of this proof, a compact implementation of the strongly polynomial-time algorithm is suggested.
Comments: 12 pages. Annotations have been added to make it more straightforward to review/read. This is a revised version of the article wherein the main lemma's proof is a proof by induction, instead of the direct proof that was used in the previous version of the article. This proof by induction is regarded by several reviewers as being clearer than the direct proof that it replaces
Subjects: Optimization and Control (math.OC)
MSC classes: Math OC
Cite as: arXiv:2410.19350 [math.OC]
  (or arXiv:2410.19350v3 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2410.19350

arXiv-issued DOI via DataCite

Submission history

From: Samuel Awoniyi [view email]
[v1] Fri, 25 Oct 2024 07:14:30 UTC (397 KB)
[v2] Tue, 20 May 2025 02:55:29 UTC (423 KB)
[v3] Tue, 16 Jun 2026 03:59:49 UTC (424 KB)

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