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 the following projects:

• SFB 568 "Strömung und Verbrennung in zukünftigen Gasturbinenbrennkammern"
• SFB 666 "Integral sheet metal design with higher order bifurcations - Development, Production, Evaluation"
• SFB 805 "Beherrschung von Unsicherheiten in laststragenden Systemen des Maschinenbaus"
• DFG Priority Programme SPP 1253 "Optimization with Partial Differential Equations"
• Center of Smart Interfaces: Understanding and Designing Fluid Boundaries (Exzellenzinitiative des Bundes)
  
• Graduate School of Computational Engineering: Beyond Traditional Sciences (Exzellenzinitiative des Bundes)
• LOEWE-Zentrum AdRIA: Adaptronik - Research, Innovation, Application