Institut für Mathematik > Mitarbeiter > Dr. Anna Thünen

Dr. Anna Thünen

Institut für Mathematik
Arbeitsgruppe Kontinuierliche Optimierung

Raum 211 / Erzstraße 1
38678 Clausthal-Zellerfeld

Telefon: +49 5323 72-2025
E-Mail: anna.thuenen@tu-clausthal.de

Vita

  • 2021 Dr.rer.nat. RWTH Aachen
  • 2017 M.Sc. Uni Magdeburg
  • 2015 B.Sc. Uni Magdeburg

Forschung

Theorie und Methoden für diskrete Strukturen in der kontinuierlichen Optimierung.

Ab hier geht es auf Englisch weiter :)

Analysis and Computation of Solutions of Continuous Optimization with Discrete Structures.

Articles and Preprints:


Proceedings and Book Chapters:


Theses:

Activities

Further Collaborations

Current Projects

  • Modern Methods for Optimization Problems with Guignard Constraint Qualification (2021-2023)
  • Most algorithms for nonlinear optimization require MFCQ or LICQ as constraint qualification. However not all problems meet this requirement, especially the large class of bilevel optimization problems. Usually regularisation or smoothing techniques are applied in these cases. The goal of this research project is to investigate modern methods and theory that do not need regularization of the problem itself.

  • Mathematical Multiscale Models for Control and Forecasting of Vehicular Traffic (2021-2022) financed by DAAD
  • The multiscale modeling technique allows the description of particle systems using methods of kinetic theory for a wide range of applications, including traffic flow, pedestrian dynamics, and swarming behavior of animals. The model classes studied in this context are: Micro-, meso-, and macroscopic models. The finest models are the microsopic ones which study every particle, e.g. a car, a pedestrian, or a bird, individually. The mesoscopic and macroscopic models zoom out and look at the overall behavior of the crowd by considering averaged quantities such as density. There are close relations between the model classes that are studied in numerous research publications but are not yet fully understood for all models and applications. We deal with a traffic model on networks and aims to match an optimal control problem on the macroscopic level to a corresponding microscopic model in order to model the junctions in the network. Theoretical investigations are accompanied by development of algorithms and numerical experiments. Further, we study a composite of two models to obtain a realistic description of traffic on a highway with both cars and trucks. This model is extended by the use of real time data and mobile sensors to adjust traffic forecasts. Both aim to reduce traffic jams and investigate how to influence traffic flow with means of optimal control and precise forecasting.

  • Multiscale Control Concepts for Transport-Dominated Problems (2020-2022)
  • In recent years, the description of controllable (or active) particle systems using methods of kinetic gas theory has been achieved and allows now to tackle a wide range of applications as for example traffic flow. In this research project, the inherent hierarchy exploited extensively in kinetic theory for theoretical and numerical considerations will be investigated in order to develop novel analytical and numerical methods for control problems posed on multiple scales as well as under aspects of non-smoothness in the control. The work program includes the analysis of consistent optimality conditions within the model hierarchies, numerical analysis for control aspects relevant in particular on the highest level of the model hierarchy, as well as the development of numerical methods for time-dynamic non-smooth optimization problems on all levels. In addition to the sensitivity of non-smooth kinetic equations, the multi-scale nature of the equations raises questions for boundary control problems of nonlocal hyperbolic equations and switching systems.

Teaching

  • Seminar: Optimization C (Continuous Optimization), Organization, summer term 2021
  • Mathematik I/II (für Bauing., Umwelting., Wirtschaftsing. FR Bau, Mobilität und Verkehr), co-Organization and exercise sessions , winter term 2017/18 - present
  • Optimization C (Continuous Optimization), Organization and exercise sessions, winter term 2020/21
  • Seminar: Differential Games, Organization, winter term 2018/19
 

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