# Semismooth* Newton Methods

## DI Michael Mandlmayr

**Nov. 5, 2019, 2:30 p.m. S2 054**

We present a new method for solving generalized equations i.e. $0\in F(x)$, where $F$ is a set valued mapping, developed by H. Gfrerer and J. Outrata. This method is based on the notion of semismooth* which, together with some suitable regularity assumption, yields local superlinear convergence of the algorithm.

The first part of the talk will introduce the listener briefly into some basics of Variational Analysis, the concept of graphical derivatives and the semismooth* property.

Secondly, a Semismooth* Newton Method will be presented for the generel case. Some of this method's novelty may be found in the fact that each iterate consists in contrast to normal Newton methods of two steps, where one is some kind of Newton step and one shall remain a mysterious motivation to join the talk.

Finally we will illustrate this concept further via the application to two important problems, namely constrained optimization and Quasi-Variational inequalities.