凸锥的闭性及Farkas引理的简短证明

IF 0.4 4区数学 Q4 MATHEMATICS

American Mathematical Monthly Pub Date : 2023-10-12 DOI:10.1080/00029890.2023.2261816

Wouter Kager

引用次数: 0

摘要

证明一个有限生成的凸锥是闭合的通常被认为是Farkas引理的几何证明中最困难的部分。我们对这一事实提供了一个简短的证明，并且(为了完整性)使用众所周知的论证从它推导出Farkas引理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A Short Simple Proof of Closedness of Convex Cones and Farkas’ Lemma

Proving that a finitely generated convex cone is closed is often considered the most difficult part of geometric proofs of Farkas’ lemma. We provide a short simple proof of this fact and (for completeness) derive Farkas’ lemma from it using well-known arguments.

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来源期刊

American Mathematical Monthly Mathematics-General Mathematics

CiteScore

0.80

自引率

20.00%

发文量

127

审稿时长

6-12 weeks

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