Nonsmooth Variational Problems and Operator Equations

Head:
Michael Hintermüller

Coworkers:
Amal Alphonse, Jo Andrea Brüggemann, Guozhi Dong, Caroline Geiersbach, Tobias Keil, Axel Kröner, Hong Nguyen, Kostas Papafitsoros, Steven-Marian Stengl

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

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 will be organizing two main scientific events in the upcoming months: A MATH+ workshop on Machine Learning in Imaging Sciences, in Weierstrass institute, May 11-13, 2020. The workshop is postponed due to corona virus. We are considering an alternative date towards the end of 2020. The 15th International Conference on Free Boundary Problems: Theory and Applications 2020 (FBP 2020), in Humboldt University (HU) of Berlin, August 31-September 4, 2020.
	March 2020: We welcome the new member of the group, Hong Nguyen.
	November 2019: We welcome the new member of the group, Dr. Axel Kröner.
	October 2019: The DFG Priority Programme 1962 Non-smooth and Complementarity-based Distributed Parameter Systems: Simulation and Hierarchical Optimization is successfully running its second phase. The annual meeting was held on October 10-12, 2019 at Hotel Sommerfeld in Kremmen and featured presentations that introduced the projects of the second period.
	August 2019: We coorganized the Sixth International Conference on Continuous Optimization (ICCOPT 2019), Berlin, August 3-8, 2019. The conference, which also included a 2-day summer school, was a great success and received very positive feedback. Apart from constituting the core of the local organization committee, our group actively participated also in the scientific part, organizing several sessions as well as giving invited and contributed talks. Congratulations also to Amal Alphonse who was selected by the best paper committee to be among the four finalists for the best paper competition.
	July 2019: We welcome the new guest member of the group, Prof. Martin Brokate.
	January 2019: We have three funded projects at the recently established Berlin Mathematics Research Center MATH+, an interdisciplinary Cluster of Excellence and cross-institutional venture of FU Berlin, HU Berlin, TU Berlin, WIAS, and Zuse Institute Berlin (ZIB): EF3-5: Direct Reconstruction of Biophysical Parameters Using Dictionary Learning and Robust Regularization (PIs: Michael Hintermüller, Tobias Schäffter) EF3-3: Optimal Transport for Imaging (PIs: Michael Hintermüller, Vladimir Spokoiny, Pavel Dvurechensky) AA4-3: Equilibria for Energy Markets with Transport (PIs: Michael Hintermüller Volker Mehrmann, Carlos Rautenberg)
	January 2018: 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.