|Publication ahead of print|
|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.
2 Département de Mathématiques, Université Montpellier, 34095 Montpellier Cedex 5, France.
3 Centro de Modelamiento Matematico, Universidad de Chile, Chile.
Corresponding author: firstname.lastname@example.org
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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