Some applications of nonnegative linear systems: Farkas strikes again

This paper presents a unifying perspective for analyzing certain systems of linear equations in nonnegative variables that arise in diverse areas of operations research: economic exchange models, finite Markov chains, directed graphs, and zero-one quadratic programs. Farkas' lemma is seen to pl...

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Bibliographic Details
Published in:Operations research letters 1994-10, Vol.16 (3), p.139-147
Main Authors: Lougee-Heimer, Robin, Adams, Warren P., Shier, Douglas R.
Format: Article
Language:English
Subjects:
Applied sciences
Exact sciences and technology
Graphs
Lagrangian duality
Linear models
Linear programming
Markov chains
Mathematical economics
Mathematical programming
Operational research and scientific management
Operational research. Management science
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Summary:This paper presents a unifying perspective for analyzing certain systems of linear equations in nonnegative variables that arise in diverse areas of operations research: economic exchange models, finite Markov chains, directed graphs, and zero-one quadratic programs. Farkas' lemma is seen to play a central role in establishing general existence, uniqueness, and positivity results. A new application involving Lagrangian duality is developed.
ISSN:0167-6377
1872-7468
DOI:10.1016/0167-6377(94)90025-6