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Linear and Multilinear Algebra Volume 63, 2015 - Issue 7
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Original Articles

Farkas-type theorems for interval linear systems

Mengxue XiaInstitute of Operational Research & Cybernetics, Hangzhou Dianzi University, Hangzhou, China.View further author information
,
Wei LiInstitute of Operational Research & Cybernetics, Hangzhou Dianzi University, Hangzhou, China.View further author information
&
Haohao LiSchool of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou, China.Correspondence[email protected]
View further author information
Pages 1390-1400 | Received 21 May 2014, Accepted 23 Jun 2014, Published online: 24 Jul 2014
 
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Abstract

We describe some Farkas-type necessary and sufficient conditions for solvability and feasibility of interval linear equations and inequalities, in a unified form. For the convenient choice in practice of theory and calculations, some different but equivalent forms of the Farkas-type conditions for interval linear systems are also discussed.

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Acknowledgements

We are grateful to an anonymous referee for his valuable comments and suggestions which led to improvements in the current version. The result of Theorem 3.2, the proofs of Theorems 3.5 and 3.6 are simplified according to his suggestions.

Additional information

Funding

The authors were partially supported by the NSF of Zhejiang Province [grant No. LY14A010028] and NNSF of China [grant No. 11171316].

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