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SPP 1962:  Nichtglatte Systeme und Komplementaritätsprobleme mit verteilten Parametern: Simulation und mehrstufige Optimierung

Fachliche Zuordnung Mathematik
Maschinenbau und Produktionstechnik
Förderung Förderung seit 2016
Projektkennung Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 274039581
 
Many of the most challenging problems in the applied sciences involve non-differentiable structures as well as partial differential operators, thus leading to non-smooth distributed parameter systems. The associated non-smoothness typically arises (1) directly in the problem formulation (through non-smooth energies/objectives or system components), (2) through inequality constraints, nonlinear complementarity or switching systems, or (3) as a result of competition and hierarchy, typically leading to multiobjective/hierarchical optimization or to quasi-variational inequality problems. In this context, the transition from smoothing or simulation based approaches to genuinely non-smooth techniques or to multi-objective respectively multi-level optimization are crucial. This motivates the research of the Priority Programme. 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 inequalitiesThe 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 The cross section of each of the envisaged research areas exhibits a spectrum from basic research projects to research addressing specific applications. Clustered around such proto-typical applications, the research is organized in three communicating research areas:Area 1: Modelling, problem analysis, algorithm design and convergence analysisArea 2: Realization of algorithms, adaptive discretization and model reductionArea 3: Incorporation of parameter dependencies and robustnessThe cross section of each of the envisaged research areas exhibits a spectrum from basic research projects to research addressing specific applications.
DFG-Verfahren Schwerpunktprogramme
Internationaler Bezug Australien, Italien, Niederlande, Schweiz, Senegal, Südafrika, USA

Projekte

Beteiligte Person Jana Segmehl
 
 

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