Math. Program., Ser. B (2018) 168:533–554
FULL LENGTH PAPER
Perturbation of error bounds
A. Y. Kruger
· M. A. López
· M. A. Théra
Received: 15 December 2015 / Accepted: 26 February 2017 / Published online: 9 March 2017
© Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2017
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 pre-
cisely, 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.
Dedicated to Professor Terry Rockafellar, one of the founders of the contemporary optimization theory,
convex analysis and variational analysis, in honor of his 80th birthday.
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.
M. A. Théra
A. Y. Kruger
M. A. López
Federation University Australia, Ballarat, Australia
Department of Statistics and Operations Research, University of Alicante, Alicante, Spain
Laboratoire XLIM, UMR-CNRS 6172, University of Limoges, Limoges, France