| Issue |
ESAIM: COCV
Volume 24, Number 2, April–June 2018
|
|
|---|---|---|
| Page(s) | 677 - 708 | |
| DOI | https://doi.org/10.1051/cocv/2017052 | |
| Published online | 26 January 2018 | |
Prox-regularity approach to generalized equations and image projection
1
Laboratoire XLIM, Université de Limoges,
123, Avenue Albert Thomas,
87060
Limoges,
Cedex, France
florent.nacry@unilim.fr
2
Département de Mathématiques, Université Montpellier,
34095
Montpellier Cedex 5, France
lionel.thibault@univ-montp2.fr
3
Centro de Modelamiento Matematico, Universidad de Chile, Chile
a Corresponding author: samir.adly@unilim.fr
Received:
9
August
2017
Accepted:
9
August
2017
In this paper, we first investigate the prox-regularity behaviour of solution mappings to generalized equations. This study is realized through a nonconvex uniform Robinson−Ursescu type theorem. Then, we derive new significant results for the preservation of prox-regularity under various and usual set operations. The role and applications of prox-regularity of solution sets of generalized equations are illustrated with dynamical systems with constraints.
Mathematics Subject Classification: 49J52 / 49J53 / 47J22 / 65K10 / 90C33
Key words: Variational analysis / prox-regular set / metric regularity / generalized equation / Robinson−Ursescu Theorem / variational inclusion / nonsmooth dynamics
© EDP Sciences, SMAI 2018
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