Characterizations of error bounds for lower semicontinuous functions on metric spaces

Dominique Azé; Jean-Noël Corvellec

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 10, Issue: 3, page 409-425
  • ISSN: 1292-8119

Abstract

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Refining the variational method introduced in Azé et al. [Nonlinear Anal. 49 (2002) 643-670], we give characterizations of the existence of so-called global and local error bounds, for lower semicontinuous functions defined on complete metric spaces. We thus provide a systematic and synthetic approach to the subject, emphasizing the special case of convex functions defined on arbitrary Banach spaces (refining the abstract part of Azé and Corvellec [SIAM J. Optim. 12 (2002) 913-927], and the characterization of the local metric regularity of closed-graph multifunctions between complete metric spaces.

How to cite

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Azé, Dominique, and Corvellec, Jean-Noël. "Characterizations of error bounds for lower semicontinuous functions on metric spaces." ESAIM: Control, Optimisation and Calculus of Variations 10.3 (2010): 409-425. <http://eudml.org/doc/90736>.

@article{Azé2010,
abstract = { Refining the variational method introduced in Azé et al. [Nonlinear Anal. 49 (2002) 643-670], we give characterizations of the existence of so-called global and local error bounds, for lower semicontinuous functions defined on complete metric spaces. We thus provide a systematic and synthetic approach to the subject, emphasizing the special case of convex functions defined on arbitrary Banach spaces (refining the abstract part of Azé and Corvellec [SIAM J. Optim. 12 (2002) 913-927], and the characterization of the local metric regularity of closed-graph multifunctions between complete metric spaces. },
author = {Azé, Dominique, Corvellec, Jean-Noël},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Error bounds; strong slope; variational principle; metric regularity.; error bounds; metric regularity},
language = {eng},
month = {3},
number = {3},
pages = {409-425},
publisher = {EDP Sciences},
title = {Characterizations of error bounds for lower semicontinuous functions on metric spaces},
url = {http://eudml.org/doc/90736},
volume = {10},
year = {2010},
}

TY - JOUR
AU - Azé, Dominique
AU - Corvellec, Jean-Noël
TI - Characterizations of error bounds for lower semicontinuous functions on metric spaces
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 10
IS - 3
SP - 409
EP - 425
AB - Refining the variational method introduced in Azé et al. [Nonlinear Anal. 49 (2002) 643-670], we give characterizations of the existence of so-called global and local error bounds, for lower semicontinuous functions defined on complete metric spaces. We thus provide a systematic and synthetic approach to the subject, emphasizing the special case of convex functions defined on arbitrary Banach spaces (refining the abstract part of Azé and Corvellec [SIAM J. Optim. 12 (2002) 913-927], and the characterization of the local metric regularity of closed-graph multifunctions between complete metric spaces.
LA - eng
KW - Error bounds; strong slope; variational principle; metric regularity.; error bounds; metric regularity
UR - http://eudml.org/doc/90736
ER -

References

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