Perturbation of error bounds

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Title: Perturbation of error bounds
Authors: Kruger, Alexander Y. | López Cerdá, Marco A. | Théra, Michel
Research Group/s: Laboratorio de Optimización (LOPT)
Center, Department or Service: Universidad de Alicante. Departamento de Matemáticas
Keywords: Error bound | Feasibility problem | Perturbation | Subdifferential | Metric regularity | Metric subregularity
Knowledge Area: Estadística e Investigación Operativa
Issue Date: Mar-2018
Publisher: Springer Berlin Heidelberg
Citation: Mathematical Programming. 2018, 168(1-2): 533-554. doi:10.1007/s10107-017-1129-4
Abstract: Our aim in the current article is to extend the developments in Kruger et al. (SIAM J Optim 20(6):3280–3296, 2010. doi: 10.1137/100782206) and, more precisely, to characterize, in the Banach space setting, the stability of the local and global error bound property of inequalities determined by lower semicontinuous functions under data perturbations. We propose new concepts of (arbitrary, convex and linear) perturbations of the given function defining the system under consideration, which turn out to be a useful tool in our analysis. The characterizations of error bounds for families of perturbations can be interpreted as estimates of the ‘radius of error bounds’. The definitions and characterizations are illustrated by examples.
Sponsor: The research is supported by the Australian Research Council: project DP160100854; EDF and the Jacques Hadamard Mathematical Foundation: Gaspard Monge Program for Optimization and Operations Research. The research of the second and third authors is also supported by MINECO of Spain and FEDER of EU: Grant MTM2014-59179-C2-1-P.
ISSN: 0025-5610 (Print) | 1436-4646 (Online)
DOI: 10.1007/s10107-017-1129-4
Language: eng
Type: info:eu-repo/semantics/article
Rights: © Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2017
Peer Review: si
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Appears in Collections:INV - LOPT - Artículos de Revistas

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