Distance to Ill-Posedness in Linear Optimization via the Fenchel-Legendre Conjugate
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Title: | Distance to Ill-Posedness in Linear Optimization via the Fenchel-Legendre Conjugate |
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Authors: | Cánovas Cánovas, María Josefa | López Cerdá, Marco A. | Parra López, Juan | Toledo, Francisco Javier |
Research Group/s: | Laboratorio de Optimización (LOPT) |
Center, Department or Service: | Universidad de Alicante. Departamento de Matemáticas |
Keywords: | Fenchel-Legendre conjugate | Stability | Well-posedness | Linear inequality systems | Distance to ill-posedness |
Knowledge Area: | Estadística e Investigación Operativa |
Issue Date: | Aug-2006 |
Publisher: | Kluwer Academic Publishers-Plenum Publishers |
Citation: | Journal of Optimization Theory and Applications. 2006, 130(2): 173-183. doi:10.1007/s10957-006-9097-5 |
Abstract: | We consider the parameter space of all the linear inequality systems, in the n-dimensional Euclidean space and with a fixed index set, endowed with the topology of the uniform convergence of the coefficient vectors. A system is ill-posed with respect to the consistency when arbitrarily small perturbations yield both consistent and inconsistent systems. In this paper, we establish a formula for measuring the distance from the nominal system to the set of ill-posed systems. To this aim, we use the Fenchel-Legendre conjugation theory and prove a refinement of the formula in Ref. 1 for the distance from any point to the boundary of a convex set. |
Sponsor: | This research has been partially supported by grants BFM2002–04114-C02 (01–02) from MEC (Spain) and FEDER (EU) and by grants GV04B-648 and GRUPOS04/79 from Generalitat Valenciana (Spain). |
URI: | http://hdl.handle.net/10045/75170 |
ISSN: | 0022-3239 (Print) | 1573-2878 (Online) |
DOI: | 10.1007/s10957-006-9097-5 |
Language: | eng |
Type: | info:eu-repo/semantics/article |
Rights: | © 2006 Springer Science + Business Media, Inc. |
Peer Review: | si |
Publisher version: | https://doi.org/10.1007/s10957-006-9097-5 |
Appears in Collections: | INV - LOPT - Artículos de Revistas |
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2006_Canovas_etal_JOptimTheoryAppl_final.pdf | Versión final (acceso restringido) | 169,93 kB | Adobe PDF | Open Request a copy |
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