Nonsmooth Variational Problems and Operator Equations

Head:
Michael Hintermüller

Coworkers:
Amal Alphonse, Jo Andrea Brüggemann, Tobias Keil, Caroline Löbhard, Kostas Papafitsoros, Ruchi Sandilya, Steven-Marian Stengl

Secretary:
Cecilia Bonetti

Guests:
Martin Brokate, Guozhi Dong, Jonas Holley, Olivier Huber, Charles Onyi

The group works in the area of mathematical modeling, in the analysis of resulting variational problems or operator equations, as well as in the development, analysis and numerical implementation of respective solution algorithms. Of key importance are hereby those processes in medicine, nature, engineering and economy, where non-smooth phenomena play a decisive role. Concretely, the research group addresses

• non-smooth models for energy functionals and/or state systems;
• (quasi) variational inequalities, or non-smooth, coupled systems and their optimal control
• equilibrium problems and game theoretical approaches.

The focus of our research is on the main application areas on quantitative biomedicine, optimization and control of technological processes, and on aspects of materials modeling. Hereby, methods in non-smooth and set-valued analysis or geometry for the handling of non-smooth systems with partial differential operators or non-smooth energies on infinite dimensional spaces are developed in order to facilitate an analytical as well as numerical exact study of the effects on non-differential elements in the underlying applications.

Research of the group and their guests is regularly presented in the research seminar.

Highlights

	We coorganized the Mathematics and Image Analysis Conference (MIA), Berlin, January 2018.
	We coordinate the DFG Priority Programme 1962 Non-smooth and Complementarity-based Distributed Parameter Systems: Simulation and Hierarchical Optimization.
	Michael Hintermüller was elected as new Chair of the Einstein Center for Mathematics Berlin (ECMath).
	Michael Hintermüller is SIAM Fellow 2016.
	Michael Hintermüller is MATHEON's executive board member.