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Priority Programme Non-smooth and Complementarity-based Distributed Parameter Systems: Simulation and Hierarchical Optimization (SPP 1962)
Deutsche Forschungsgemeinschaft (DFG)
The goals of the programme are to:
- lay the analytical foundations (through, e.g., the advancement of non-smooth and set-valued analysis)
- establish a basis for stable numerical approximation through the design of algorithms with mesh independent convergence
- address the influence of parameters, which enter the above-mentioned problems and which fall into a specified parameter range (uncertainty set)
The overall research of the Priority Programme aims at combining non-smooth (numerical) analysis of non-linear complementarity, quasi-variational inequality and hierarchical optimization problems, the development, analysis and realization of robust solution algorithms, and applications of large-scale and infinite-dimensional problems where non-smoothness/switching occurs in or are due to:
- systems governing an optimization problem
- lower level problems of bi- or multilevel equilibrium problems
- coupled systems of equilibrium problems (in particular (generalized) Nash games)
- systems that require robust solutions
- quasi-variational inequalities
The research of the Priority Programme will be validated against prototypical applications. These include:
- multi-physics problems such as frictional elasto-plastic contact problems in a dynamic regime and coupled with thermal effects
- motion optimization and optimal system design in robotics and biomechanics
- multi-objective control systems such as (generalized) Nash equilibrium problems in technical or life sciences as well as in economics
Clustered around such proto-typical applications, the research is organized in three communicating research areas:
Area 1: Modelling, problem analysis, algorithm design and convergence analysis
Area 2: Realization of algorithms, adaptive discretization and model reduction
Area 3: Incorporation of parameter dependencies and robustness

Institute for Mathematics
Humboldt-University of Berlin
10099 Berlin
Prof. Dr. Michael Hintermüller
phone +49 30 2093-2668
e-mail: hint@math.hu-berlin.de

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