- Tytuł:
- Proximal-based regularization methods and successive approximation of variational inequalities in Hilbert spaces
- Autorzy:
-
Kaplan, A.
Tichatschke, R. - Powiązania:
- https://bibliotekanauki.pl/articles/205832.pdf
- Data publikacji:
- 2002
- Wydawca:
- Polska Akademia Nauk. Instytut Badań Systemowych PAN
- Tematy:
-
funkcja Bregmana
metoda punktów proksymalnych
nierówność wariacyjna
operator monotoniczny
regularyzacja
Bregman function
monotone operators
proximal point methods
regularization
variational inequalities - Opis:
- For variational inequalities with multi-valued, maximal monotone operators in Hilbert spaces we study proximal-based methods with an improvement of the data approximation after each (approximately performed) proximal iteration. The standard conditions on a distance functional of Bregman's type are weakened, depending on a "reserve of monotonicity" of the operator in the variational inequality, and the enlargement concept is used for approximating the operator. Weak convergence of the proxinnal iterates to a solution of tire original problem is proved. The construction of the [epsilon]-enlargement of monotone operators is analyzed for some particular cases.
- Źródło:
-
Control and Cybernetics; 2002, 31, 3; 521-544
0324-8569 - Pojawia się w:
- Control and Cybernetics
- Dostawca treści:
- Biblioteka Nauki
Artykuł