Optimization methods for mathematical programs with equilibrium constraints in function spaces based on adaptive error control and reduced order or low rank tensor approximations
Description
Publications
AnneTherese Rauls, Stefan Ulbrich: Subgradient Computation for the Solution Operator of the Obstacle Problem , SIAM J. Control Optim. 575, pp. 32233248, 2019 (SPP1962056).
Preprints
Sebastian Garreis, Thomas M. Surowiec, Michael Ulbrich: An InteriorPoint Approach for Solving RiskAverse PDEConstrained Optimization Problems with Coherent Risk Measures (SPP1962111, 04/2019, [bib])
Lukas Hertlein, Michael Ulbrich: An Inexact Bundle Algorithm for Nonconvex Nondifferentiable Functions in Hilbert Space (SPP1962084, 10/2018, [bib])
AnneTherese Rauls, Gerd Wachsmuth: Generalized Derivatives for the Solution Operator of the Obstacle Problem (SPP1962057, 06/2018, [bib])
AnneTherese Rauls, Stefan Ulbrich: Subgradient Computation for the Solution Operator of the Obstacle Problem (SPP1962056, 05/2018, [bib])
Research Area
Modeling, problem analysis, algorithm design and convergence analysis
The focus of this area is on the development and analysis of genuinely nonsmooth models in the sciences in order to properly capture realworld effects and to avoid comprising smoothing approaches. In simulation and optimization this requires to advance setvalued analysis and the design of robust algorithms for nonsmooth problems.Realization of algorithms, adaptive discretization and model reduction
As the target applications of this SPP involve nonsmooth structures and partial differential operators, the discretization of the associated problems and robust error estimation are important issues to be address, and proper modelreduction 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.Members
Project Related News

Oct 12, 2018 : New preprint submitted
Lukas Hertlein submitted the preprint SPP1962084, 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
AnneTherese Rauls joins Project 23