Phase 1 of the SPP1962 ran from October 2016 to October 2019 and has been superseded by the current phase.

List of projects in Phase 1

  • Approximation of Monge-Kantorovich Problems
    S. Bartels
  • Coupling Hyperbolic PDEs with Switched DAEs: Analysis, Numerics and Application to Blood Flow Models
    R. Borsche, S. Trenn
  • Numerical Methods for Diagnosis and Therapy Design of Cerebral Palsy by Bilevel Optimal Control of Constrained Biomechanical Multi-Body Systems
    H. Bock, E. Kostina
  • Parameter Identification in Models With Sharp Phase Transitions
    C. Clason, A. Rösch
  • Multiobjective Optimal Control of Partial Differential Equations Using Reduced-Order Modeling
    M. Dellnitz, S. Volkwein
  • Analysis and Solution Methods for Bilevel Optimal Control Problems
    S. Dempe, G. Wachsmuth
  • Identification of Energies from Observations of Evolutions
    M. Fornasier
  • A Calculus for Non-Smooth Shape Optimization with Applications to Geometric Inverse Problems
    R. Herzog, S. Schmidt
  • Optimal Control of Dissipative Solids: Viscosity Limits and Non-Smooth Algorithms
    D. Knees , C. Meyer, R. Herzog
  • Generalized Nash Equilibrium Problems with Partial Differential Operators: Theory, Algorithms, and Risk Aversion
    M. Hintermüller , T. Surowiec
  • Optimal Control of Elliptic and Parabolic Quasi-Variational Inequalities
    M. Hintermüller
  • Coordination Funds
    M. Hintermüller
  • Simulation and Control of a Nonsmooth Cahn-Hilliard Navier–Stokes System with Variable Fluid Densities
    M. Hintermüller , M. Hinze
  • Algorithms for Quasi-Variational Inequalities in Infinite-Dimensional Spaces
    C. Kanzow, D. Wachsmuth
  • Non-smooth Methods for Complementarity Formulations of Switched Advection-Diffusion Processes
    C. Kirches , S. Sager
  • Optimal Control of Variational Inequalities of the Second Kind with Application to Yield Stress Fluids
    C. Meyer, B. Schweizer, S. Turek
  • 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
  • Optimizing Variational Inequalities on Shape Manifolds
    V. Schulz
  • Multi-Leader-Follower Games in Function Space
    A. Schwartz, S. Steffensen
  • Stress-Based Methods for Variational Inequalities in Solid Mechanics: Finite Element Discretization and Solution by Hierarchical Optimization
    G. Starke
  • 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
  • Optimization of Non-smooth Hyperbolic Maxwell's Equations in Type-II Superconductivity Based on the Bean Critical State Model
    I. Yousept

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.