{"title":"A simple algebraic proof of Farkas's lemma and related theorems","authors":"C. G. Broyden","doi":"10.1080/10556789808805676","DOIUrl":null,"url":null,"abstract":"A proof is given of Farkas's lemma based on a new theorem pertaining to orthogodal matrices. It is claimed that this theorem is slightly more general than Tucker's theorem, which concerns skew-symmetric matrices and which may itself be derived simply from tne new theorem. Farkas's lemma and other theorems of the alternative then follow trivially from Tucker's theorem","PeriodicalId":54673,"journal":{"name":"Optimization Methods & Software","volume":"107 5 1","pages":"185-199"},"PeriodicalIF":1.4000,"publicationDate":"1998-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"33","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Optimization Methods & Software","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1080/10556789808805676","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, SOFTWARE ENGINEERING","Score":null,"Total":0}
引用次数: 33
Abstract
A proof is given of Farkas's lemma based on a new theorem pertaining to orthogodal matrices. It is claimed that this theorem is slightly more general than Tucker's theorem, which concerns skew-symmetric matrices and which may itself be derived simply from tne new theorem. Farkas's lemma and other theorems of the alternative then follow trivially from Tucker's theorem
期刊介绍：
Optimization Methods and Software
publishes refereed papers on the latest developments in the theory and realization of optimization methods, with particular emphasis on the interface between software development and algorithm design.
Topics include:
Theory, implementation and performance evaluation of algorithms and computer codes for linear, nonlinear, discrete, stochastic optimization and optimal control. This includes in particular conic, semi-definite, mixed integer, network, non-smooth, multi-objective and global optimization by deterministic or nondeterministic algorithms.
Algorithms and software for complementarity, variational inequalities and equilibrium problems, and also for solving inverse problems, systems of nonlinear equations and the numerical study of parameter dependent operators.
Various aspects of efficient and user-friendly implementations: e.g. automatic differentiation, massively parallel optimization, distributed computing, on-line algorithms, error sensitivity and validity analysis, problem scaling, stopping criteria and symbolic numeric interfaces.
Theoretical studies with clear potential for applications and successful applications of specially adapted optimization methods and software to fields like engineering, machine learning, data mining, economics, finance, biology, or medicine. These submissions should not consist solely of the straightforward use of standard optimization techniques.
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