{"title":"Duality theory in linear optimization and its extensions -- formally verified","authors":"Martin Dvorak, Vladimir Kolmogorov","doi":"arxiv-2409.08119","DOIUrl":null,"url":null,"abstract":"Farkas established that a system of linear inequalities has a solution if and\nonly if we cannot obtain a contradiction by taking a linear combination of the\ninequalities. We state and formally prove several Farkas-like theorems over\nlinearly ordered fields in Lean 4. Furthermore, we extend duality theory to the\ncase when some coefficients are allowed to take ``infinite values''.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Optimization and Control","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.08119","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
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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