Metric subregularity of order q and the solving of inclusions

Michaël Gaydu; Michel Geoffroy; Célia Jean-Alexis

Open Mathematics (2011)

  • Volume: 9, Issue: 1, page 147-161
  • ISSN: 2391-5455

Abstract

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We consider some metric regularity properties of order q for set-valued mappings and we establish several characterizations of these concepts in terms of Hölder-like properties of the inverses of the mappings considered. In addition, we show that even if these properties are weaker than the classical notions of regularity for set-valued maps, they allow us to solve variational inclusions under mild assumptions.

How to cite

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Michaël Gaydu, Michel Geoffroy, and Célia Jean-Alexis. "Metric subregularity of order q and the solving of inclusions." Open Mathematics 9.1 (2011): 147-161. <http://eudml.org/doc/269641>.

@article{MichaëlGaydu2011,
abstract = {We consider some metric regularity properties of order q for set-valued mappings and we establish several characterizations of these concepts in terms of Hölder-like properties of the inverses of the mappings considered. In addition, we show that even if these properties are weaker than the classical notions of regularity for set-valued maps, they allow us to solve variational inclusions under mild assumptions.},
author = {Michaël Gaydu, Michel Geoffroy, Célia Jean-Alexis},
journal = {Open Mathematics},
keywords = {Metric regularity of order q; Calmness of order q; Hölder metric regularity; Covering property; Variational inclusions; Successive approximations; metric regularity of order ; calmness of order ; covering property; variational inclusions; successive approximations},
language = {eng},
number = {1},
pages = {147-161},
title = {Metric subregularity of order q and the solving of inclusions},
url = {http://eudml.org/doc/269641},
volume = {9},
year = {2011},
}

TY - JOUR
AU - Michaël Gaydu
AU - Michel Geoffroy
AU - Célia Jean-Alexis
TI - Metric subregularity of order q and the solving of inclusions
JO - Open Mathematics
PY - 2011
VL - 9
IS - 1
SP - 147
EP - 161
AB - We consider some metric regularity properties of order q for set-valued mappings and we establish several characterizations of these concepts in terms of Hölder-like properties of the inverses of the mappings considered. In addition, we show that even if these properties are weaker than the classical notions of regularity for set-valued maps, they allow us to solve variational inclusions under mild assumptions.
LA - eng
KW - Metric regularity of order q; Calmness of order q; Hölder metric regularity; Covering property; Variational inclusions; Successive approximations; metric regularity of order ; calmness of order ; covering property; variational inclusions; successive approximations
UR - http://eudml.org/doc/269641
ER -

References

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