Optimization methods for mathematical programs with equilibrium constraints in function spaces based on adaptive error control and reduced order or low rank tensor approximations
Anne-Therese Rauls, Stefan Ulbrich: Subgradient Computation for the Solution Operator of the Obstacle Problem , SIAM J. Control Optim. 57-5, pp. 3223-3248, 2019 (SPP1962-056).
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