Results 91 to 100 of about 123 (108)

On a characterization of Clarke's tangent cone

Journal of Optimization Theory and Applications, 1992
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G Giorgi
exaly   +4 more sources

Nonsmooth Milyutin-Dubovitskii Theory and Clarke's Tangent Cone

Mathematics of Operations Research, 1986
In optimization theory the idea of approximating nonconvex sets by convex cones which satisfy an abstract condition—the Intersection Principle—is due to Milyutin and Dubovitskii. This approach has been successfully applied to optimization problems with differentiable data.
exaly   +2 more sources

Clarke's tangent cones and the boundaries of closed sets in Rn

Nonlinear Analysis: Theory, Methods & Applications, 1979
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 $k$.
exaly   +2 more sources

Weak Clarke epiderivative in set-valued optimization [PDF]

Journal of Mathematical Analysis and Applications, 2008
A new notion of weak Clarke epiderivative for a set-valued map is introduced using the concept of Clarke tangent cone. The existence, characterization and properties of weak Clarke epiderivative are then studied.
C S Lalitha
exaly   +2 more sources

Characterization of Clarke's tangent and normal cones in finite and infinite dimensions

Nonlinear Analysis: Theory, Methods & Applications, 1983
exaly   +3 more sources

Tangent cones and Clarke subdifferential

2023
openaire   +1 more source

On the notion of tangent cone in mathematical programming

Optimization, 1992
G Giorgi
exaly  

On the Intersection of a Clarke Cone with a Boltyanskii Cone

SIAM Journal on Control and Optimization, 2007
Alberto Bressan
exaly  

Generalized Clarke Epiderivatives of Parametric Vector Optimization Problems

Journal of Optimization Theory and Applications, 2010
J C Yao, Chuong T D, Yao J C
exaly  

Variants of the Ekeland Variational Principle for a set-valued map involving the Clarke Normal Cone

Journal of Mathematical Analysis and Applications, 2006
Truong Xuân Dúc Ha
exaly