Journal article
Extending the mixed algebraic-analysis Fourier-Motzkin elimination method for classifying linear semi-infinite programmes
Optimization, Vol.65(4), pp.707-727
04/02/2016
DOI: 10.1080/02331934.2015.1080254
Abstract
Motivated by a recent Basu-Martin-Ryan paper, we obtain a reduced primal-dual pair of a linear semi-infinite programming problem by applying an amended Fourier-Motzkin elimination method to the linear semi-infinite inequality system. The reduced primal-dual pair is equivalent to the original one in terms of consistency, optimal values and asymptotic consistency. Working with this reduced pair and reformulating a linear semi-infinite programme as a linear programme over a convex cone, we reproduce all the theorems that lead to the full eleven possible duality state classification theory. Establishing classification results with the Fourier-Motzkin method means that the two classification theorems for linear semi-infinite programming, 1969 and 1974, have been proved by new and exciting methods. We also show in this paper that the approach to study linear semi-infinite programming using Fourier-Motzkin elimination is not purely algebraic, it is mixed algebraic-analysis.
Details
- Title: Subtitle
- Extending the mixed algebraic-analysis Fourier-Motzkin elimination method for classifying linear semi-infinite programmes
- Creators
- K.O. Kortanek - University of PittsburghQinghong Zhang - Northern Michigan University
- Resource Type
- Journal article
- Publication Details
- Optimization, Vol.65(4), pp.707-727
- DOI
- 10.1080/02331934.2015.1080254
- ISSN
- 0233-1934
- eISSN
- 1029-4945
- Publisher
- Taylor & Francis
- Number of pages
- 21
- Language
- English
- Date published
- 04/02/2016
- Academic Unit
- Business Analytics
- Record Identifier
- 9984963216002771
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