Projects in the research area: Realization of algorithms, adaptive discretization and model reduction

  • Numerical Methods for Diagnosis and Therapy Design of Cerebral Palsy by Bilevel Optimal Control of Constrained Biomechanical Multi-Body Systems
    H. Bock, E. Kostina
  • Analysis and Solution Methods for Bilevel Optimal Control Problems
    S. Dempe, G. Wachsmuth
  • A Calculus for Non-Smooth Shape Optimization with Applications to Geometric Inverse Problems
    R. Herzog, S. Schmidt
  • Optimal Control of Elliptic and Parabolic Quasi-Variational Inequalities
    M. Hintermüller
  • Simulation and Control of a Nonsmooth Cahn-Hilliard Navier–Stokes System with Variable Fluid Densities
    M. Hintermüller , M. Hinze
  • Optimizing Fracture Propagation Using a Phase-Field Approach
    I. Neitzel, W. Wollner
  • Optimal Control of Static Contact in Finite Strain Elasticity
    A. Schiela
  • Shape Optimization for Maxwell's Equations Including Hysteresis Effects in the Material Laws
    S. Schmidt, A. Walther
  • Multi-Leader-Follower Games in Function Space
    A. Schwartz, S. Steffensen
  • Optimization methods for mathematical programs with equilibrium constraints in function spaces based on adaptive error control and reduced order or low rank tensor approximations
    M. Ulbrich, S. Ulbrich

Communicating Research Areas

  • Modeling, problem analysis, algorithm design and convergence analysis

    The focus of this area is on the development and analysis of genuinely non-smooth models in the sciences in order to properly capture real-world effects and to avoid comprising smoothing approaches. In simulation and optimization this requires to advance set-valued analysis and the design of robust algorithms for non-smooth problems.

  • Realization of algorithms, adaptive discretization and model reduction

    As the target applications of this SPP involve non-smooth structures and partial differential operators, the discretization of the associated problems and robust error estimation are important issues to be address, and proper model-reduction techniques need to be developed.

  • Incorporation of parameter dependencies and robustness

    In many applications the robustness of solutions with respect to a given parameter range (uncertainty set) is highly relevant. Correspondingly, in this research area of the SPP, bi- or multilevel optimization approaches will be studied in order to robustify problem solutions against uncertain parameters.