Proximal-based regularization methods and successive approximation of variational inequalities in Hilbert spaces

• Autorzy: Kaplan A. , Tichatschke R.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Bregman function; monotone operators; proximal point methods; regularization; variational inequalities

PL

funkcja Bregmana; metoda punktów proksymalnych; nierówność wariacyjna; operator monotoniczny; regularyzacja

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2002
• Tom: Vol. 31, no 3
• Strony: 521--544
• Opis fizyczny: Bibliogr. 35 poz.,

Twórcy

autor

Kaplan A.

• Dept. of Mathematics, University of Trier, D-54286 Trier

autor

Tichatschke R.

• Dept. of Mathematics, University of Trier, D-54286 Trier

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