- Tytuł:
- On a globalization property
- Autorzy:
- Rolewicz, Stefan
- Powiązania:
- https://bibliotekanauki.pl/articles/1340680.pdf
- Data publikacji:
- 1993
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
Φ-subgradients
globalization property - Opis:
- Let (X,τ) be a topological space. Let Φ be a class of real-valued functions defined on X. A function ϕ ∈ Φ is called a local Φ-subgradient of a function f:X → ℝ at a point $x_0$ if there is a neighbourhood U of $x_0$ such that f(x) - f($x_0$) ≥ ϕ(x) - ϕ($x_0$) for all x ∈ U. A function ϕ ∈ Φ is called a global Φ-subgradient of f at $x_0$ if the inequality holds for all x ∈ X. The following properties of the class Φ are investigated: (a) when the existence of a local Φ-subgradient of a function f at each point implies the existence of a global Φ-subgradient of f at each point (globalization property), (b) when each local Φ-subgradient can be extended to a global Φ-subgradient (strong globalization property).
- Źródło:
-
Applicationes Mathematicae; 1993-1995, 22, 1; 69-73
1233-7234 - Pojawia się w:
- Applicationes Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł