Stability of the Duality Gap in Linear Optimization
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http://hdl.handle.net/10045/67778
Title: | Stability of the Duality Gap in Linear Optimization |
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Authors: | Goberna, Miguel A. | Ridolfi, Andrea Beatriz | Vera de Serio, Virginia N. |
Research Group/s: | Laboratorio de Optimización (LOPT) |
Center, Department or Service: | Universidad de Alicante. Departamento de Matemáticas |
Keywords: | Linear programming | Linear semi-infinite programming | Duality gap function | Stability | Primal-dual partition |
Knowledge Area: | Estadística e Investigación Operativa |
Issue Date: | 6-Mar-2017 |
Publisher: | Springer Science+Business Media Dordrecht |
Citation: | Set-Valued and Variational Analysis. 2017. doi:10.1007/s11228-017-0405-z |
Abstract: | In this paper we consider the duality gap function g that measures the difference between the optimal values of the primal problem and of the dual problem in linear programming and in linear semi-infinite programming. We analyze its behavior when the data defining these problems may be perturbed, considering seven different scenarios. In particular we find some stability results by proving that, under mild conditions, either the duality gap of the perturbed problems is zero or + ∞ around the given data, or g has an infinite jump at it. We also give conditions guaranteeing that those data providing a finite duality gap are limits of sequences of data providing zero duality gap for sufficiently small perturbations, which is a generic result. |
Sponsor: | This research was partially supported by MINECO of Spain and FEDER of EU, Grant MTM2014-59179-C2-01 and SECTyP-UNCuyo Res. 4540/13-R. |
URI: | http://hdl.handle.net/10045/67778 |
ISSN: | 1877-0533 (Print) | 1877-0541 (Online) |
DOI: | 10.1007/s11228-017-0405-z |
Language: | eng |
Type: | info:eu-repo/semantics/article |
Rights: | © Springer Science+Business Media Dordrecht 2017. |
Peer Review: | si |
Publisher version: | http://dx.doi.org/10.1007/s11228-017-0405-z |
Appears in Collections: | INV - LOPT - Artículos de Revistas |
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2017_Goberna_etal_Set-ValuedVarAnal_final.pdf | Versión final (acceso restringido) | 321,68 kB | Adobe PDF | Open Request a copy |
2017_Goberna_etal_Set-ValuedVarAnal_preprint.pdf | Preprint (acceso abierto) | 1,06 MB | Adobe PDF | Open Preview |
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