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Adresse (Briefe):

Technische Universität Dortmund
Fak. Mathematik, LS X
44221 Dortmund

Adresse (Lieferungen):

Technische Universität Dortmund
Fak. Mathematik, LS X
Vogelpothsweg 87
44227 Dortmund


Telefonnummern und Email-Adressen:

Fr. C. Mecke (Sekretariat):
(+49) 231 / 755-5411

Prof. Dr. H. Blum:
(+49) 231 / 755-5410

Prof. Dr. Ch. Kreuzer:
(+49) 231 / 755-5425

Prof. Dr. Ch. Meyer:
(+49) 231 / 755-5412

Fax: (+49) 231 / 755-5416


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Summer School (July, 30, — August, 01, 2018)

Complementarity problems in Applied Mathematics: Modeling, Analysis, and Optimization

funded by

DFG SPP 1962 "Non-smooth and Complementarity-based Distributed Parameter Systems: Simulation and Hierarchical Optimization”



Summary

Complementarity problems and related non-smooth structures play an important role in various applications such as elastoplastic deformation or damage processes. The non-smoothness of such systems has a direct impact on its mathematical treatment, beginning from the analysis over numerical simulations to the optimization of such systems and processes. The summer school aims to illustrate these effects on applied mathematics as a whole. It is primarily intended for the doctoral and postdoctoral students of the DFG SPP1962, however other interested parties may also apply to register.



Speakers


Venue
The summer school will take place at the Faculty of Mathematics, TU Dortmund.

Address:
Vogelpothsweg 87,
44227 Dortmund
Germany

How to get there
There is a direct connection via local train from Dortmund main station to the university. Just take the local train S1 into direction Düsseldorf or Solingen and exit at „Dortmund Universität“.

Important Dates
Registration: June, 30, 2018
Begin: July, 30, 2018, noon
End: August, 01, 2018, noon

Fees
There is no registration fee, but registration is mandatory. Please note that travel costs and accommodation will not be provided by us.

Registration
In order to register, please write an email to Christan Meyer.

Accomodation
A hotel nearby the university:
There are several hotels and hostels nearby the main station, for instance:

Program
  • Juan Carlos de los Reyes - Optimal control of variational inequalities of the second kind

    Abstract:
    Variational inequalities are an important mathematical tool for modelling free boundary problems that arise in different application areas. In this short course we will focus on a class of variational inequalities, called of the second kind, and start by giving an overview of the most prominent application examples of these types of variational inequalities, and the related analytical and numerical difficulties. The lectures will focus thereafter on the optimal control of these variational inequalities. We will present in depth the different techniques for proving existence of Lagrange multipliers and the different types of optimality systems that can be derived for the characterization of optimal controls. Different stationarity concepts will be introduced in this context and the gap between finite- and infinite-dimensional problems will be addressed. The concepts will be illustrated by means of different finite- and infinite-dimensional toy examples.
    Lecture notes



  • Rene Henrion - M-stationarity conditions for MPECs in finite dimension

    Abstract:
    The derivation of necessary optimality conditions for Mathematical Programs with Equilibrium Constraints (MPECs) or coupled versions thereof (EPECs) inevitably leads to the application of tools from nonsmooth and variational analysis. The purpose of this lecture is an introduction into the concept, application and verification of so-called M-stationarity conditions which are based on the generalized differential calculus in the sense of Mordukhovich. Basic tools and calculus rules will be provided in a gentle way. Some emphasis will be put on the verification of the so-called calmness (a set-valued Lipschitz like concept) of the canonical perturbation mapping for generalized equations. The results will be applied to an electricity spot market model.
    Lecture notes


  • Chiara Zanini - Rate-independent modeling in fracture mechanics: a vanishing viscosity approach

    Abstract:
    In the first part we address the question of the rate-independent modeling of a fracture process. From a mathematical point of view, the first solution concept was defined via global minimization: (global) energetic solution and its relation with the notion of quasistatic evolution will be discussed. The energetic solution approach is not satisfactory for the study of the propagation of a fracture and therefore, in the second part, we introduce a different solution concept, via vanishing viscosity, and discuss how to prove existence.
    Lecture notes