Perturbation of error bounds

Full Length Paper Series B

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.

Keywords

Error bound Feasibility problem Perturbation Subdifferential Metric regularity Metric subregularity 

Mathematics Subject Classification

49J52 49J53 90C30 

Notes

Acknowledgements

The authors thank the referees for the careful reading of the manuscript and many constructive comments and suggestions. We particularly thank one of the reviewers for attracting our attention to [26, Theorem 3.2] and [47, Theorem 4.4].

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Copyright information

© Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2017

Authors and Affiliations

  1. 1.Federation University AustraliaBallaratAustralia
  2. 2.Department of Statistics and Operations ResearchUniversity of AlicanteAlicanteSpain
  3. 3.Laboratoire XLIM, UMR-CNRS 6172University of LimogesLimogesFrance

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