Variational Analysis in Semi-Infinite and Infinite Programming, I: Stability of Linear Inequality Systems of Feasible Solutions
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http://hdl.handle.net/10045/75133
Títol: | Variational Analysis in Semi-Infinite and Infinite Programming, I: Stability of Linear Inequality Systems of Feasible Solutions |
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Autors: | Cánovas Cánovas, María Josefa | López Cerdá, Marco A. | Mordukhovich, Boris S. | Parra López, Juan |
Grups d'investigació o GITE: | Laboratorio de Optimización (LOPT) |
Centre, Departament o Servei: | Universidad de Alicante. Departamento de Matemáticas |
Paraules clau: | Semi-infinite and infinite programming | Variational analysis | Linear infinite inequality systems | Robust stability | Generalized differentiation | Coderivatives |
Àrees de coneixement: | Estadística e Investigación Operativa |
Data de publicació: | 16-de desembre-2009 |
Editor: | Society for Industrial and Applied Mathematics (SIAM) |
Citació bibliogràfica: | SIAM Journal on Optimization. 2009, 20(3): 1504-1526. doi:10.1137/090765948 |
Resum: | This paper concerns applications of advanced techniques of variational analysis and generalized differentiation to parametric problems of semi-infinite and infinite programming, where decision variables run over finite-dimensional and infinite-dimensional spaces, respectively. Part I is primarily devoted to the study of robust Lipschitzian stability of feasible solutions maps for such problems described by parameterized systems of infinitely many linear inequalities in Banach spaces of decision variables indexed by an arbitrary set T. The parameter space of admissible perturbations under consideration is formed by all bounded functions on T equipped with the standard supremum norm. Unless the index set T is finite, this space is intrinsically infinite-dimensional (nonreflexive and nonseparable) of the l∞ type. By using advanced tools of variational analysis and exploiting specific features of linear infinite systems, we establish complete characterizations of robust Lipschitzian stability entirely via their initial data with computing the exact bound of Lipschitzian moduli. A crucial part of our analysis addresses the precise computation of the coderivative of the feasible set mapping and its norm. The results obtained are new in both semi-infinite and infinite frameworks. (A correction to the this article has been appended at the end of the pdf file.) |
Patrocinadors: | This research was partially supported by grants MTM2005-08572-C03 (01-02) from MEC (Spain) and FEDER (EU), MTM2008-06695-C03 (01-02) from MICINN (Spain), and ACOMP/2009/047&133 from Generalitat Valenciana (Spain); National Science Foundation (USA) under grant DMS-0603846. |
URI: | http://hdl.handle.net/10045/75133 |
ISSN: | 1052-6234 (Print) | 1095-7189 (Online) |
DOI: | 10.1137/090765948 |
Idioma: | eng |
Tipus: | info:eu-repo/semantics/article |
Drets: | © 2009 Society for Industrial and Applied Mathematics |
Revisió científica: | si |
Versió de l'editor: | https://doi.org/10.1137/090765948 |
Apareix a la col·lecció: | INV - LOPT - Artículos de Revistas |
Arxius per aquest ítem:
Arxiu | Descripció | Tamany | Format | |
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2009_Canovas_etal_SIAMJOptim.pdf | 505,08 kB | Adobe PDF | Obrir Vista prèvia | |
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