# Nonlinear Optimization

Nonlinear Optimization is nowadays an important technology in applied mathematics, science and engineering. Nonlinear optimization problems appear in many applications, e.g., shape optimization in engineering, robust portfolio optimization in finance, parameter identification, optimal control, etc., and Nonlinear Optimization has emerged as a key technology in modern scientific and industrial applications. Challenging are in particular optimization problems with partial differential equations as constraints (PDE-constraints), for example optimization problems for flows, transport problems, diffusion processes, wave propagation or mechanical structures. An efficient solution of such problems requires highly developed optimization methods, which use modern adaptive multilevel techniques of scientific computing.

The research group Nonlinear Optimization considers the development, theory, implementation and application of efficient algorithms for nonlinear optimization. Particular research topics are PDE-constrained optimization, large scale optimization, adaptive multilevel techniques, preconditioning, global optimization and relaxation of discrete problems.

The research group Nonlinear Optimization is engaged among others in the following projects:

- Profile Area Thermo-Fluids & Interfaces (TFI)
- Profile Area “From Material to Product Innovation” (PMP)
- TRR 154 “Mathematical Modelling, Simulation and Optimization on the Example of Gas Networks”
- SFB 805 “Beherrschung von Unsicherheiten in lasttragenden Systemen des Maschinenbaus”
- SFB 1194 “Interaction between Transport and Wetting Processes”
- DFG Priority Programme SPP 1962 “Non-smooth and Complementarity-based Distributed Parameter Systems: Simulation and Hierarchical Optimization”
- Graduate School of Computational Engineering: Beyond Traditional Sciences(Exzellenzinitiative des Bundes)
- Graduate School of Energy Science and Engineering(Exzellenzinitiative des Bundes)
- IRTG 1529 “Mathematical Fluid Dynamics”
- DFG Schwerpunktprogramm 1748 “Reliable Simulation Techniques in Solid Mechanics. Development of Non-standard Discretization Methods, Mechanical and Mathematical Analysis”