The department of Decision-Making Theory organizes a Mini-Symposium dedicated to three exceptional speakers: Silvia Carpitella, Tobias Boege, and Michael Mandlmayr. The Mini-Symposium is organized in a hybrid form. It is possible to participate either in person or connect virtually using the Zoom application.
The symposium will be held at UTIA, in Lecture hall No. 3 accessible from the lobby, on September 13, 2021, starting at 14:00.
ABSTRACT - We present the application of the general semismooth* Newton method, introduced by Gfrerer and Outrata, to three challenging problems:
The novelty of this method is, that these problems are interpreted as generalized equations. This means that for a set valued function we are interested in finding a point, such that the image contains zero.
As the method is called a “Newton”-method, to fulfill the expectations some linearization has to happen at some point of the graph. The linearization of a set valued mapping is done via a so-called normalcones to the graph, loosely speaking this normalcone can be seen as a generalization of normals. Furthermore, we need to have suitable point for the linearization. In contrast to the well known newton method for functions, where for an iteration point x we just take (x,F(x)), for set valued mappings the choice is not trivial and is done in a so-called Approximation step.
So this method consists of two parts:
We will show that under suitable assumptions this method converges locally superlinear to the solution. Moreover, we will illustrate the construction of such a method for the Quasi-Variational Inequalities and Coloumb Friction. Also, we will present numerical evidence for this convergence speed.