Primal-dual stability in continuous linear optimization
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Title: | Primal-dual stability in continuous linear optimization |
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Authors: | Goberna, Miguel A. | Todorov, Maxim I. |
Research Group/s: | Programación Semi-infinita |
Center, Department or Service: | Universidad de Alicante. Departamento de Estadística e Investigación Operativa | Universidad de las Américas Puebla. Departamento de Física y Matemáticas |
Keywords: | Linear programming | Linear semi-infinite programming | Stability |
Knowledge Area: | Estadística e Investigación Operativa |
Issue Date: | 28-Apr-2007 |
Publisher: | Springer |
Citation: | GOBERNA TORRENT, Miguel Ángel; TODOROV, Maxim I. “Primal-dual stability in continuous linear optimization”. Mathematical Programming. Vol. 116, No. 1-2 (2009). ISSN 0025-5610, pp. 129-146 |
Abstract: | Any linear (ordinary or semi-infinite) optimization problem, and also its dual problem, can be classified as either inconsistent or bounded or unbounded, giving rise to nine duality states, three of them being precluded by the weak duality theorem. The remaining six duality states are possible in linear semi-infinite programming whereas two of them are precluded in linear programming as a consequence of the existence theorem and the non-homogeneous Farkas Lemma. This paper characterizes the linear programs and the continuous linear semi-infinite programs whose duality state is preserved by sufficiently small perturbations of all the data. Moreover, it shows that almost all linear programs satisfy this stability property. |
Sponsor: | This research was supported by DGES and FEDER, Grant MTM2005-08572-C03-01 and partially supported by CONACyT of MX.Grant 44003. |
URI: | http://hdl.handle.net/10045/15403 |
ISSN: | 0025-5610 |
DOI: | 10.1007/s10107-007-0128-2 |
Language: | eng |
Type: | info:eu-repo/semantics/article |
Rights: | The original publication is available at www.springerlink.com |
Peer Review: | si |
Publisher version: | http://dx.doi.org/10.1007/s10107-007-0128-2 |
Appears in Collections: | INV - LOPT - Artículos de Revistas |
Files in This Item:
File | Description | Size | Format | |
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Goberna_Primal-dual_Rev.pdf | Versión revisada (acceso libre) | 206,95 kB | Adobe PDF | Open Preview |
Goberna_Primal-dual_Final.pdf | Versión final (acceso restringido) | 251,37 kB | Adobe PDF | Open Request a copy |
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