Lipschitz Continuity of the Optimal Value via Bounds on the Optimal Set in Linear Semi-Infinite Optimization
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Título: | Lipschitz Continuity of the Optimal Value via Bounds on the Optimal Set in Linear Semi-Infinite Optimization |
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Autor/es: | Cánovas Cánovas, María Josefa | López Cerdá, Marco A. | Parra López, Juan | Toledo, Francisco Javier |
Grupo/s de investigación o GITE: | Laboratorio de Optimización (LOPT) |
Centro, Departamento o Servicio: | Universidad de Alicante. Departamento de Matemáticas |
Palabras clave: | Lipschitz continuity of the optimal value | Boundedness of the optimal set | Distance to ill-posedness | Linear semi-infinite programming |
Área/s de conocimiento: | Estadística e Investigación Operativa |
Fecha de publicación: | ago-2006 |
Editor: | INFORMS |
Cita bibliográfica: | Mathematics of Operations Research. 2006, 31(3): 478-489. doi:10.1287/moor.1060.0198 |
Resumen: | We consider the parametric space of all the linear semi-infinite programming problems with constraint systems having the same index set. Under a certain regularity condition, the so-called well-posedness with respect to the solvability, it is known from Cánovas et al. [2] that the optimal value function is Lipschitz continuous around the nominal problem π. In this paper we obtain an explicit Lipschitz constant for such a function in a certain neighborhood of π. We emphasize the fact that both the constant and the size of the neighborhood are exclusively expressed in terms of the nominal problem data, and that they involve the distances to primal and to dual inconsistency. Moreover, a uniform bound for the optimal set is provided. This bound constitutes a key ingredient to derive the Lipschitz constant for the optimal value function. |
Patrocinador/es: | This research has been partially supported by Grants BFM2002-04114-C02 (01-02) and MTM2005-08572-C03 (01-02) from MEC (Spain) and FEDER (E.U.) and GV04B-648, GRUPOS04/79, ACOMP06/203, and ACOMP06/117 from Generalitat Valenciana (Spain). |
URI: | http://hdl.handle.net/10045/75608 |
ISSN: | 0364-765X (Print) | 1526-5471 (Online) |
DOI: | 10.1287/moor.1060.0198 |
Idioma: | eng |
Tipo: | info:eu-repo/semantics/article |
Derechos: | © 2006, INFORMS |
Revisión científica: | si |
Versión del editor: | https://doi.org/10.1287/moor.1060.0198 |
Aparece en las colecciones: | INV - LOPT - Artículos de Revistas |
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2006_Canovas_etal_MathOperRes_final.pdf | Versión final (acceso restringido) | 359,67 kB | Adobe PDF | Abrir Solicitar una copia |
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