Search results for "Subsmooth sets"

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Contribution to variational analysis : stability of tangent and normal cones and convexity of Chebyshev sets

2014

The aim of this thesis is to study the following three problems: 1) We are concerned with the behavior of normal cones and subdifferentials with respect to two types of convergence of sets and functions: Mosco and Attouch-Wets convergences. Our analysis is devoted to proximal, Fréchet, and Mordukhovich limiting normal cones and subdifferentials. The results obtained can be seen as extensions of Attouch theorem to the context of non-convex functions on locally uniformly convex Banach space. 2) For a given bornology β on a Banach space X we are interested in the validity of the following "lim inf" formula (…).Here Tβ(C; x) and Tc(C; x) denote the β-tangent cone and the Clarke tangent cone to …

Contingent coneCône tangent de BouligandSuite minimisanteFonctions sous-régulières cône normal (tangent) de ClarkeClarke tangent (normal) coneMetric projection[MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM]Chebyshev setMosco (Attouch-Wets) convergenceAsplund spaceCône normal proximalProjection metriqueEnsemble de ChebyshevConvergence au sens de Mosco (d'Attouch-Wets)Subsmooth sets (functions)BornologyBornologieMinimizing sequenceProximal normal coneFréchet (Mordukhovich limiting) subdifferentialEspace d'AsplundTrustworthinessSous-différentiel de Fréchet (de Mordukhovich)Ensembles sous-réguliers
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Regularization of perturbed state-dependent sweeping processes with nonregular sets

2018

International audience; In this paper, we prove the convergence strongly pointwisely (up to a subsequence) of Moreau-Yosida regularization of perturbed state-dependent sweeping process with nonregular (subsmooth and positively alpha-far) sets in separable Hilbert spaces. Some relevant consequences are indicated.

Positively alpha-far sets[MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM]MSC: 34A60 49J52 34G25 49J53Moreau-Yosida regularizationDifferential inclusions[MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM]Subsmooth setsSweeping processClarke normal cone
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