Non-Smooth and Complementarity-Based Distributed Parameter Systems
Description
Many of the most challenging problems in the applied sciences involve non-differentiable structures as well as partial differential operators, thus leading to non-smooth distributed parameter systems. This edited volume aims to establish a theoretical and numerical foundation and develop new algorithmic paradigms for the treatment of non-smooth phenomena and associated parameter influences. Other goals include the realization and further advancement of these concepts in the context of robust and hierarchical optimization, partial differential games, and nonlinear partial differential complementarity problems, as well as their validation in the context of complex applications. Areas for which applications are considered include optimal control of multiphase fluids and of superconductors, image processing, thermoforming, and the formation of rivers and networks.
Chapters are written by leading researchers and present results obtained in the second funding phase of the DFG Special Priority Program on Nonsmooth and Complementarity Based Distributed Parameter Systems: Simulation and Hierarchical Optimization that ran from 2019 to 2025.
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Content
Chapter 1. Numerical Approximation of Optimal Convex Shapes in R3.- Chapter 2. Multiobjective Optimization of Non-Smooth PDE-Constrained Problems.- Chapter 3. Bilevel Optimal Control: Theory, Algorithms, and Applications.- Chapter 4. Identification of Stress in Heterogeneous Contact Models.- Chapter 5. Multi-scale control concepts for transport-dominated problems.- Chapter 6. A Calculus for Non-Smooth Shape Optimization with Applications to Geometric Inverse Problems.- Chapter 7. Shape optimisation in the Lipschitz topology.- Chapter 8. Constrained Mean Field Games: Analysis and Algorithms.- Chapter 9. Analysis and stationarity for risk-averse optimisation with variational inequality constraints.- Chapter 10. Non-monotone proximal gradient methods in infinite-dimensional spaces with applications to non-smooth optimal control problems.- Chapter 11. Non-uniform Grid Refinement for the Combinatorial Integral Approximation.- Chapter 12. Simulation and Optimal Control of Rate-independent Systems with Non-Convex Energies.- Chapter 13. Quadratic Regularization of Bilevel Optimal Transport Problems in In-/Finite Dimensions.- Chapter 14. Coefficient Control of Variational Inequalities.- Chapter 15. Nonsmooth Multi-Level Optimization Algorithms for Energetic Formulations of Finite-Strain Elastoplasticity.- Chapter 16. Optimal transport networks and their duals.- Chapter 17. Shape & Topology Optimization for the Mitigation of Coastal Erosion.- Chapter 18. Shape optimization in the space of piecewise-smooth shapes for the Bingham flow variational inequality.- Chapter 19. Theory and Solution Methods for Generalized Nash Equilibrium Problems with Application to Networks of Nonlinear Hyperbolic Conservation Laws.- Chapter 20. Regularity Result for Hyperbolic Maxwell Quasi-Variational Inequalities in Type-II Superconductivity.