线性优化及其扩展中的对偶理论 -- 正式验证

arXiv - MATH - Optimization and Control Pub Date : 2024-09-12 DOI:arxiv-2409.08119

Martin Dvorak, Vladimir Kolmogorov

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引用次数: 0

摘要

法卡斯认为，线性不等式系统有一个解，前提是我们不能通过线性组合得到矛盾。我们在精益 4 中阐述并正式证明了几个类似法卡斯的线性有序域定理。此外，我们还将对偶理论扩展到允许某些系数取 "无限值 "的情况。

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Duality theory in linear optimization and its extensions -- formally verified

Farkas established that a system of linear inequalities has a solution if and only if we cannot obtain a contradiction by taking a linear combination of the inequalities. We state and formally prove several Farkas-like theorems over linearly ordered fields in Lean 4. Furthermore, we extend duality theory to the case when some coefficients are allowed to take ``infinite values''.

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arXiv - MATH - Optimization and Control

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