The group's main focus is on the application driven development of optimization methods, the close connection to machine learning, and an efficient implementation on computers. We believe in the potential of multi-disciplinary cooperation between partners with a profound disciplinary expertise and value the mutual benefit for both sides: novel, innovative approaches and insights in the application field by means of optimization; and a demand/feedback effect that stimulates the development of new methodologies in applied mathematics.Active research fields include
- optimization and machine learning,
- optimization for clinical decision support and training,
- direct methods for (global) optimal control of PDEs, DAEs or ODEs,
- in particular for mixed-integer optimal control, see this recent talk about PDE constrained mixed-integer optimal control for an overview,
- direct methods for parameter estimation, experimental design, and inverse simulation for nonlinear processes,
- structure exploiting QP solvers for real-time optimization,
- optimization under uncertainty, e.g., with stochastic differential equations,
- and mixed-integer nonlinear programming.
Main application areas are found in Medicine, Mobility, Energy and Chemical Engineering, and Economics. Challenging problems in these areas are treated in interdisciplinary cooperations with scientists from academia and industry. We are also interest in the question, how mathematical optimization relates to human decision making, compare the page on Complex Problem Solving.
Members of the group have been involved in industrial projects, e.g., with ABB, Air Berlin, BASF, Daimler, Deutsche Lufthansa, and Volkswagen. Industrial relevance of our mathematical and computational optimization algorithms is of utmost importance, and we are open for new collaborations.Some current and finished projects are included in the research programs
- DFG Research Training Group 2297 MathCoRe,
- BMBF program Mathematik für Innovationen with the project Power to Chemicals, P2Chem,
- DFG Priority Programme SPP 1962 Non-smooth and Complementarity-based Distributed Parameter Systems: Simulation and Hierarchical Optimization,
- The ERC Consolidator 2014 Grant Mathematical Optimization for Clinical Decision Support and Training
- BMBF program Mathematik für Innovation in Industrie und Dienstleistungen (Nichtlineare gemischt-ganzzahlige Optimierung und optimale Steuerung stark gekoppelter Industrieprozesse, GOSSIP),
- DFG Priority Programme SPP1253 PDE Optimization,
- Embedded Optimization for Resource Constrained Platforms (EMBOCON) within the EU FP7.
Furthermore we appreciate research funding from the Klaus-Tschira-Stiftung, the Center for Dynamic Systems, and the International Max Planck Research School Magdeburg.
A (somewhat outdated) description of the group's research activities is available as a pdf file.