Prox-regularity approach to generalized equations and image projection
ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 2, pp. 677-708.

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.

DOI : 10.1051/cocv/2017052
Classification : 49J52, 49J53, 47J22, 65K10, 90C33
Mots-clés : Variational analysis, prox-regular set, metric regularity, generalized equation, Robinson−Ursescu Theorem, variational inclusion, nonsmooth dynamics
Adly, Samir 1 ; Nacry, Florent 1 ; Thibault, Lionel 1

1 
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Adly, Samir; Nacry, Florent; Thibault, Lionel. Prox-regularity approach to generalized equations and image projection. ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 2, pp. 677-708. doi : 10.1051/cocv/2017052. http://archive.numdam.org/articles/10.1051/cocv/2017052/

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