Quantitative stability of linear infinite inequality systems under block perturbations with applications to convex systems
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Título: | Quantitative stability of linear infinite inequality systems under block perturbations with applications to convex systems |
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Autor/es: | Cánovas Cánovas, María Josefa | López Cerdá, Marco A. | Mordukhovich, Boris S. | Parra López, Juan |
Grupo/s de investigación o GITE: | Laboratorio de Optimización (LOPT) |
Centro, Departamento o Servicio: | Universidad de Alicante. Departamento de Estadística e Investigación Operativa |
Palabras clave: | Semi-infinite and infinite programming | Parametric optimization | Variational analysis | Convex infinite inequality systems | Quantitative stability | Lipschitzian bounds | Generalized differentiation | Coderivatives | Block perturbations |
Área/s de conocimiento: | Estadística e Investigación Operativa |
Fecha de publicación: | 21-sep-2011 |
Editor: | Springer |
Cita bibliográfica: | TOP. 2012, 20(2): 310-327. doi:10.1007/s11750-011-0226-4 |
Resumen: | The original motivation for this paper was to provide an efficient quantitative analysis of convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional (resp. finite-dimensional) Banach spaces and that are indexed by an arbitrary fixed set J. Parameter perturbations on the right-hand side of the inequalities are required to be merely bounded, and thus the natural parameter space is l ∞(J). Our basic strategy consists of linearizing the parameterized convex system via splitting convex inequalities into linear ones by using the Fenchel–Legendre conjugate. This approach yields that arbitrary bounded right-hand side perturbations of the convex system turn on constant-by-blocks perturbations in the linearized system. Based on advanced variational analysis, we derive a precise formula for computing the exact Lipschitzian bound of the feasible solution map of block-perturbed linear systems, which involves only the system’s data, and then show that this exact bound agrees with the coderivative norm of the aforementioned mapping. In this way we extend to the convex setting the results of Cánovas et al. (SIAM J. Optim. 20, 1504–1526, 2009) developed for arbitrary perturbations with no block structure in the linear framework under the boundedness assumption on the system’s coefficients. The latter boundedness assumption is removed in this paper when the decision space is reflexive. The last section provides the aimed application to the convex case. |
Patrocinador/es: | This research was partially supported by grants MTM2008-06695-C03 (01-02) from MICINN (Spain). The research of M.A. López was partially supported by ARC Project DP110102011 from Australia. The research of B.S. Mordukhovich was partially supported the US National Science Foundation under grants DMS-0603848 and DMS-1007132. |
URI: | http://hdl.handle.net/10045/33782 |
ISSN: | 1134-5764 (Print) | 1863-8279 (Online) |
DOI: | 10.1007/s11750-011-0226-4 |
Idioma: | eng |
Tipo: | info:eu-repo/semantics/article |
Derechos: | The original publication is available at http://www.springerlink.com |
Revisión científica: | si |
Versión del editor: | http://dx.doi.org/10.1007/s11750-011-0226-4 |
Aparece en las colecciones: | INV - LOPT - Artículos de Revistas |
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2012_Canovas_etal_TOP-pre.pdf | Preprint (acceso abierto) | 184,48 kB | Adobe PDF | Abrir Vista previa |
2012_Canovas_etal_TOP.pdf | Versión final (acceso restringido) | 641,06 kB | Adobe PDF | Abrir Solicitar una copia |
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