List of all projects
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P01Approximation of Non-Smooth Optimal Convex Shapes with Applications in Optimal Insulation and Minimal Resistance
S. Bartels, G. Wachsmuth -
P02Multiobjective Optimization of Non-Smooth PDE-Constrained Problems — Switches, State Constraints and Model Order Reduction
M. Dellnitz, S. Volkwein, S. Peitz -
P03Bilevel Optimal Control: Theory, Algorithms, and Applications
G. Wachsmuth, S. Dempe -
P04Identification of Stresses in Heterogeneous Contact Models
G. Duda, A. Schiela, M. Weiser -
P05Multiscale Control Concepts for Transport-Dominated Problems
S. Göttlich, M. Banda, M. Herty -
P06A Calculus for Non-Smooth Shape Optimization with Applications to Geometric Inverse Problems
R. Herzog, S. Schmidt -
P07Coordination Funds
M. Hintermüller -
P08A Non-Smooth Phase-Field Approach to Shape Optimization with Instationary Fluid Flow
M. Hintermüller, M. Hinze -
P09Constrained Mean Field Games: Analysis and Algorithms
M. Hintermüller, T. Surowiec -
P10A Unified Approach to Optimal Uncertainty Quantification and Risk-Averse Optimization with Quasi-Variational Inequality Constraints
M. Hintermüller -
P11Optimization Problems in Banach Spaces with Non-Smooth Structure
C. Kanzow, D. Wachsmuth -
P12Non-Smooth Methods for Complementarity Formulations of Switched Advection-Diffusion Processes
C. Kirches, S. Sager -
P13Simulation and Optimization of Rate-Independent Systems with Non-Convex Energies
D. Knees, C. Meyer -
P14Bilevel Optimal Transport
D. Lorenz, C. Meyer -
P15Optimizing Fracture Propagation using a Phase-Field Approach
I. Neitzel, T. Wick, W. Wollner -
P16Nonsmooth Multi-Level Optimization Algorithms for Energetic Formulations of Finite-Strain Elastoplasticity
O. Sander, A. Schiela -
P17Nonsmooth and Nonconvex Optimal Transport Problems
B. Schmitzer, B. Wirth -
P18Shape Optimization for Mitigating Coastal Erosion
V. Schulz, D. Seck -
P19Semi-Smooth Newton Methods on Shape Spaces
V. Schulz, K. Welker -
P20Stress-Based Methods for Variational Inequalities in Solid Mechanics: Finite Element Discretization and Solution by Hierarchical Optimization
G. Starke, R. Krause -
P21Theory and Solution Methods for Generalized Nash Equilibrium Problems Governed by Networks of Nonlinear Hyperbolic Conservation Laws
S. Ulbrich, M. Ulbrich -
P22Multi-Physics Phenomena in High-Temperature Superconductivity: Analysis, Numerics and Optimization
I. Yousept
Communicating Research Areas
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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.
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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.
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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.