## 15. ÖMG-Kongress

Jahrestagung der Deutschen Mathematikervereinigung

#### 16. bis 22. September 2001 in Wien

**Sektion 10 - Angewandte Mathematik, Industrie- und Finanzmathematik**

Freitag, 21. September 2001, 15.30, Hörsaal 42

**Iterative regularization and application of variational inequalities in Hilbert spaces**
**Rainer Tichatschke**, **Universität Trier**
(Koautor: A. Kaplan)

A general approach for analyzing convergence of proximal-like
methods for variational inequalities with set-valued maximal
monotone operators is developed.

This approach is devoted to
methods coupling successive approximation of the variational
inequality with the proximal point algorithm as well as to related
methods using regularization on a subspace and/or weak
regularization.

The convergence results are proved under mild
assumptions with respect to the original variational inequality
and admit, in particular, the use of the -enlargement of an
operator. Also conditions providing linear convergence are
established.

Taking into
account the specific structure of non-differentiable terms in
energy functionals of several problems in mathematical physics,
we analyse the construction of
-enlargements for some special operators.

As an application of the general scheme, a proximal-based variant of the
elliptic regularization method is considered.

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