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Projects in the research area: Modeling, problem analysis, algorithm design and convergence analysis

  • Multiobjective Optimization of Non-Smooth PDE-Constrained Problems — Switches, State Constraints and Model Order Reduction
  • Bilevel Optimal Control: Theory, Algorithms, and Applications
  • Multiscale Control Concepts for Transport-Dominated Problems
  • Optimization Problems in Banach Spaces with Non-Smooth Structure
  • Simulation and Optimization of Rate-Independent Systems with Non-Convex Energies
  • Bilevel Optimal Transport
  • Nonsmooth and Nonconvex Optimal Transport Problems
  • Stress-Based Methods for Variational Inequalities in Solid Mechanics: Finite Element Discretization and Solution by Hierarchical Optimization
  • Theory and Solution Methods for Generalized Nash Equilibrium Problems Governed by Networks of Nonlinear Hyperbolic Conservation Laws

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.