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 ofClarke 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 definitionbut it is equivalent to it.
Publié le : 1979-07-04
Classification:
optimality conditions,
sub-differential calculus,
Lipschitzian functions,
Tangent cones,
normal cones,
generalized gradients,
[MATH]Mathematics [math]
@article{hal-01552475,
author = {Rockafellar, Ralph, },
title = {Clarke's tangent cones and the boundaries of closed sets in $\mathbb{R}^n$},
journal = {HAL},
volume = {1979},
number = {0},
year = {1979},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-01552475}
}
Rockafellar, Ralph, . Clarke's tangent cones and the boundaries of closed sets in $\mathbb{R}^n$. HAL, Tome 1979 (1979) no. 0, . http://gdmltest.u-ga.fr/item/hal-01552475/