Enhanced metric regularity and Lipschitzian properties of variational systems

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Title: Enhanced metric regularity and Lipschitzian properties of variational systems
Authors: Aragón Artacho, Francisco Javier | Mordukhovich, Boris S.
Research Group/s: Laboratorio de Optimización (LOPT)
Center, Department or Service: Universidad de Alicante. Departamento de Estadística e Investigación Operativa
Keywords: Variational analysis and optimization | Parametric variational systems | Generalized equations | Set-valued mappings | Metric regularity | Lipschitzian properties
Knowledge Area: Estadística e Investigación Operativa | Análisis Matemático
Issue Date: 1-Mar-2011
Publisher: Springer Science+Business Media, LLC
Citation: ARAGÓN ARTACHO, Francisco J.; MORDUKHOVICH, Boris S. "Enhanced metric regularity and Lipschitzian properties of variational systems". Journal of Global Optimization. Vol. 50, Issue 1 (May 2011). ISSN 0925-5001, pp. 145-167
Abstract: This paper mainly concerns the study of a large class of variational systems governed by parametric generalized equations, which encompass variational and hemivariational inequalities, complementarity problems, first-order optimality conditions, and other optimization-related models important for optimization theory and applications. An efficient approach to these issues has been developed in our preceding work (Aragón Artacho and Mordukhovich in Nonlinear Anal 72:1149–1170, 2010) establishing qualitative and quantitative relationships between conventional metric regularity/subregularity and Lipschitzian/calmness properties in the framework of parametric generalized equations in arbitrary Banach spaces. This paper provides, on one hand, significant extensions of the major results in op.cit. to partial metric regularity and to the new hemiregularity property. On the other hand, we establish enhanced relationships between certain strong counterparts of metric regularity/hemiregularity and single-valued Lipschitzian localizations. The results obtained are new in both finite-dimensional and infinite-dimensional settings.
Sponsor: Research of the first author was partially supported by MICINN of Spain, grant MTM2008-06695-C03-01 and program “Juan de la Cierva”. Research of the second author was partially supported by the US National Science Foundation under grants DMS-0603846 and DMS-1007132 and by the Australian Research Council under grant DP-12092508.
URI: http://hdl.handle.net/10045/29037
ISSN: 0925-5001 (Print) | 1573-2916 (Online)
DOI: 10.1007/s10898-011-9698-x
Language: eng
Type: info:eu-repo/semantics/article
Rights: The original publication is available at www.springerlink.com
Peer Review: si
Publisher version: http://dx.doi.org/10.1007/s10898-011-9698-x
Appears in Collections:INV - LOPT - Artículos de Revistas

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