Search results for "cône normal"
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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 …
Differential inclusions involving normal cones of nonregular sets in Hilbert spaces
2017
This thesis is dedicated to the study of differential inclusions involving normal cones of nonregular sets in Hilbert spaces. In particular, we are interested in the sweeping process and its variants. The sweeping process is a constrained differential inclusion involving normal cones which appears naturally in several applications such as elastoplasticity, electrical circuits, hysteresis, crowd motion, etc.This work is divided conceptually in three parts: Study of positively alpha-far sets, existence results for differential inclusions involving normal cones and characterizations of Lyapunov pairs for the sweeping process. In the first part (Chapter 2), we investigate the class of positivel…