Nonsmooth Variational Problems and Operator Equations

Head:
Michael Hintermüller

Coworkers:
Amal Alphonse, Marcelo Bongarti, Sarah Essadi, Maximilian Fröhlich, Denis Korolev, Ioannis Papadopoulos, Felix Sauer, Clemens Sirotenko, Qi Wang

Team Assistant:
Pia Pfau

Guests:
Martin Brokate

From left to right: Michael Hintermüller, Amal Alphonse, Marcelo Bongarti, Sarah Essadi, Felix Sauer, Clemens Sirotenko, Pia Pfau, Maximilian Fröhlich, Qi Wang, Ioannis Papadopoulos, Denis Korolev.

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.

The group and their guests regularly present their work in the » research seminars.

Highlights

	October 2024: Caroline Geiersbach has accepted a call of the University Hamburg. We congratulate her on her professorship in the Department of Mathematics (Optimisation under Uncertainty).
	October 2024: In collaboration with IVW and RPTU "Scientific Computing" the BMBF project "Flexible, resilient and efficient multi-scale simulation using hybridisation of established numerical solvers with physically-informed neural networks (HybridSolver)" was launched.
	September 2024: Michael Hintermüller was co-organiser of Varana 2024 (Variational Analysis and Applications), the 77th course of the International School of Mathematics "Guido Stampacchia" in Erice, Italy.
	August 2024: At the IFIP TC7 Konferenz in Hamburg, Amal Alphonse and Marcelo Bongarti organised the mini-symposium "Modeling, Analysis and Optimal Control of Infinite Dimensional Problems and Applications".
	June 2024: Michael Hintermüller was invited speaker at the One World Optimization Seminar" in Vienna, Austria, and gave the talk "Quasi-variational inequalities: Semismooth Newton methods, optimal control, and uncertainties".
	March 2024: As an invited speaker at the conference "Recent Advances in Scientific Computing and Inverse Problems" at the PolyU Hongkong, China, Michael Hintermüller gave the talk "PDE-constrained optimization with learning-informed structures".
	September 2023: Two projects started at RG8: “Approximating combinatorial optimization problems” and “Classical-quantum time-sharing and variational manifolds” within the Einstein Research Unit on Quantum Devices, a joint programme with the Berlin University Alliance.
	May 2023: The workshop Frontiers of Stochastic Optimization and its Applications in Industry was held at the WIAS. It was co-organized and supported by RG 8.
	April 2023: The MATH+ project AA4-13: Equilibria for Distributed Multi-Modal Energy Systems under Uncertainty has started.
	March 2023: The semi-annual meeting for TRR154 members took place in Berlin. The meeting was jointly organized with the FAU Erlangen-Nuremberg, with support from the Humboldt University Berlin.
	February 2023: The RG 8 was co-organizer and supporter of the Mathematics and Image Analysis Conference (MIA) in Berlin, together with Humboldt Universität zu Berlin and TU Berlin.
	January 2023: We congratulate Steven-Marian Stengl who successfully defended his PhD thesis entitled “Existence Theorems, Stationarity Conditions and Adaptive Numerical Methods for Generalized Nash Equilibrium Problems Constrainted by Partial Differential Equations".
	December 2022: Jo Andrea Brüggemann successfully defended her PhD thesis entitled “A Class of Elliptic Obstacle-Type Quasi-Variational Inequalities with an Additional Volume Constraint: Theory and Solution Methods". Congratulations!
	November 2022: Michael Hintermüller was elected speaker of MATH+.
	October 2022: The annual meeting of SPP1962 Non-smooth and Complementarity-based Distributed Parameter Systems: Simulation and Hierarchical Optimization, held in the center of Berlin, was well attended and appreciated. A special issue book collecting the research achievements of the second phase of the SPP is being compiled for publication under Birkhäuser.
	July 2022: Two projects of the Collaborative Research Center SFB TRR 154 in phase three (2022 - 2026) have started: B02: Multicriteria optimization using the example of gas markets C08: Stochastic gradient methods
	April 2022: The MATH+ project started: EF1-15: Robust multilevel training for artificial neural networks January 2022: Two new MATH+ projects started: EF1-17: Data-driven robust model predictive control under distribution shift EF3-12: Integrated learning and variational methods for quantitative dynamic imaging January 2022: The joint research project Machine Learning for Simulation Intelligence in Composite Process Design (ML4Sim) is starting. The project is funded by the Leibniz Association, following success in the Leibniz competition. October 2021: The Thematic Einstein Semester on Mathematics of Imaging in Real-World Challenges of Mathematics Research Center MATH+ took place in Berlin. Co-organized by RG 8 it consisted of a kick-off workshop, three plenary tandem talks, three tutorials, and a hackathon event, concluding with the SIAM Conference on Imaging Science in March 2022.
	September 2021: The 15th International Conference on Free Boundary Problems: Theory and Applications 2021 (FBP 2021) took place from September 13 - 17, 2021, after having been originally planned for September 2020. Michael Hintermüller was the Chair of the Organizing Commitee with several members of the group being in the Local Support Team.
	March 2021: The SPP 1962 Non-smooth and Complementarity-based Distributed Parameter Systems: Simulation and Hierarchical Optimization continues to run successfully with a large number of preprints, and the annual meeting was held virtually in March 2021. Furthermore, a special issue book collecting the research achievements of the first phase of the SPP is being compiled for publication under Birkhäuser, giving each project in the SPP an opportunity to condense and provide an overview of their work.
	February 2021: Michael Hintermüller co-organized the hybrid workshop on Challenges in Optimization with Complex PDE-Systems at the MFO, Oberwolfach Research Institute for Mathematics. Olivier Huber, Amal Alphonse, and Caroline Geiersbach were invited to give talks.
	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.
	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).
	October 2016: We coordinate the DFG Priority Programme 1962 Non-smooth and Complementarity-based Distributed Parameter Systems: Simulation and Hierarchical Optimization.