Optimization methods for mathematical programs with equilibrium constraints in function spaces based on adaptive error control and reduced order or low rank tensor approximations
No publications from this project yet.
Sebastian Garreis, Thomas M. Surowiec, Michael Ulbrich: An Interior-Point Approach for Solving Risk-Averse PDE-Constrained Optimization Problems with Coherent Risk Measures (SPP1962-111, 04/2019, [bib])
Lukas Hertlein, Michael Ulbrich: An Inexact Bundle Algorithm for Nonconvex Nondifferentiable Functions in Hilbert Space (SPP1962-084, 10/2018, [bib])
Anne-Therese Rauls, Gerd Wachsmuth: Generalized Derivatives for the Solution Operator of the Obstacle Problem (SPP1962-057, 06/2018, [bib])
Anne-Therese Rauls, Stefan Ulbrich: Subgradient Computation for the Solution Operator of the Obstacle Problem (SPP1962-056, 05/2018, [bib])
Modeling, problem analysis, algorithm design and convergence analysisThe 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 reductionAs 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 robustnessIn 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.
Project Related News
Oct 12, 2018 : New preprint submitted
Lukas Hertlein submitted the preprint SPP1962-084, An Inexact Bundle Algorithm for Nonconvex Nondifferentiable Functions in Hilbert Space
Oct 10, 2016 : Welcome to our new project member
Lukas Hertlein joins project 23.
Aug 18, 2016 : Welcome to our new project member
Anne-Therese Rauls joins Project 23