Article Dans Une Revue Nonlinear Analysis: Theory, Methods and Applications Année : 1979

Clarke's tangent cones and the boundaries of closed sets in $\mathbb{R}^n$

Résumé

Let $C$ be a nonempty closed subset of $\mathbb{R}^n$. For each $x \in C$, the tangent cone $T_C(x)$ in the sense of Clarke consists of all $y \in \mathbb{R}^n$ such that, whenever one has sequences $t_k\downarrow 0$ and $x_k \rightarrow x$ with $x_k \in C$, there exist $y_k \rightarrow y$ with $x_k + t_ky_k \in C$ for all $k$. This is not Clarke’s original definition but it is equivalent to it.

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hal-01552475 , version 1 (03-07-2017)

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Ralph Tyrrell Rockafellar. Clarke's tangent cones and the boundaries of closed sets in $\mathbb{R}^n$. Nonlinear Analysis: Theory, Methods and Applications, 1979, 3, pp.145-154. ⟨10.1016/0362-546X(79)90044-0⟩. ⟨hal-01552475⟩
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