Analysis and Solution Methods for Bilevel Optimal Control Problems
Description
Publications
Constantin Christof, Gerd Wachsmuth: Differential Sensitivity Analysis of Variational Inequalities with Locally Lipschitz Continuous Solution Operators, Applied Mathematics & Optimization, 2019 (SPP1962039).
Stephan Dempe, Felix Harder, Patrick Mehlitz, Gerd Wachsmuth: Solving inverse optimal control problems via value functions to global optimality, J Glob Optim, 2019 (SPP1962066).
AnneTherese Rauls, Gerd Wachsmuth: Generalized Derivatives for the Solution Operator of the Obstacle Problem, SetValued Var. Anal , 2019 (SPP1962057).
Yu Deng, Patrick Mehlitz, Uwe Prüfert: Optimal control in firstorder Sobolev spaces with inequality constraints, Comput Optim Appl, 2019 (SPP1962053).
Patrick Mehlitz: On the Sequential Normal Compactness Condition and its Restrictiveness in Selected Function Spaces, SetValued and Variational Analysis , 2018 (SPP1962025).
Felix Harder, Gerd Wachsmuth: Comparison of Optimality Systems for the Optimal Control of the Obstacle Problem , GAMM‐Mitteilungen, 40: 312338., 2018 (SPP1962029).
Constantin Christof, Gerd Wachsmuth: On the NonPolyhedricity of Sets with Upper and Lower Bounds in Dual Spaces, GAMM‐Mitteilungen, 40: 339350., 2018 (SPP1962031).
Constantin Christof, Gerd Wachsmuth: NoGap SecondOrder Conditions via a Directional Curvature Functional, SIAM J. Optim., 28(3), 2097–2130. , 2018 (SPP1962026).
Marc Herrmann, Roland Herzog, Stephan Schmidt, Josè Vidal, Gerd Wachsmuth: Discrete Total Variation with Finite Elements and Applications to Imaging, J Math Imaging Vis, 2018 (SPP1962054).
Felix Harder: Legendre forms in reflexive Banach spaces, Zeitschrift für Analysis und ihre Anwendungen (ZAA), 2018 (SPP1962030).
Felix Harder, Gerd Wachsmuth: The limiting normal cone of a complementarity set in Sobolev spaces, Optimization, 2018 (SPP1962023).
Felix Harder, Gerd Wachsmuth: Optimality conditions for a class of inverse optimal control problems with partial differential equations, Optimization, 2018 (SPP1962048).
Ulisse Stefanelli, Daniel Wachsmuth, Gerd Wachsmuth: Optimal control of a rateindependent evolution equation via viscous regularization, Discrete and Continuous Dynamical Systems  Series S 10(6), 14671485 , 2017 (SPP1962001).
Patrick Mehlitz, Gerd Wachsmuth: The Weak Sequential Closure of Decomposable Sets in Lebesgue Spaces and its Application to Variational Geometry , SetValued and Variational Analysis , 2017 (SPP1962016).
Patrick Mehlitz, Gerd Wachsmuth: The Limiting Normal Cone to Pointwise Defined Sets in Lebesgue Spaces, SetValued and Variational Analysis, 2016 (SPP1962004).
Preprints
Gerd Wachsmuth: Elliptic QuasiVariational Inequalities under a Smallness Assumption: Uniqueness, Differential Stability and Optimal Control (SPP1962118, 09/2019, [bib])
Constantin Christof, Gerd Wachsmuth: On SecondOrder Optimality Conditions for Optimal Control Problems Governed by the Obstacle Problem (SPP1962113, 06/2019, [bib])
Tobias Geiger, Daniel Wachsmuth, Gerd Wachsmuth: Optimal Control of ODEs with State Suprema (SPP1962094, 10/2018, [bib])
Sören Bartels, Gerd Wachsmuth: Numerical Approximation of Optimal Convex Shapes (SPP1962089, 10/2018, [bib])
Tommy Etling, Roland Herzog, Estefanía Loayza, Gerd Wachsmuth: First and Second Order Shape Optimization Based on Restricted Mesh Deformations (SPP1962088, 10/2018, [bib])
Christian Clason, Yu Deng, Patrick Mehlitz, Uwe Prüfert: Optimal Control Problems with Control Complementarity Constraints (SPP1962081, 10/2018, [bib])
Stephan Dempe, Patrick Mehlitz: Semivectorial Bilevel Programming versus Scalar Bilevel Programming (SPP1962082, 10/2018, [bib])
Stephan Dempe, Felix Harder, Patrick Mehlitz, Gerd Wachsmuth: Solving Inverse Optimal Control Problems via Value Functions to Global Optimality (SPP1962066, 07/2018, [bib])
AnneTherese Rauls, Gerd Wachsmuth: Generalized Derivatives for the Solution Operator of the Obstacle Problem (SPP1962057, 06/2018, [bib])
Marc Herrmann, Roland Herzog, Stephan Schmidt, Josè Vidal, Gerd Wachsmuth: Discrete Total Variation with Finite Elements and Applications to Imaging (SPP1962054, 04/2018, [bib])
Yu Deng, Patrick Mehlitz, Uwe Prüfert: Optimal Control in Firstorder Sobolev Spaces with Inequality Constraints (SPP1962053, 04/2018, [bib])
Yu Deng, Patrick Mehlitz, Uwe Prüfert: On an Optimal Control Problem with Gradient Constraints (SPP1962050, 02/2018, [bib])
Felix Harder, Gerd Wachsmuth: Optimality Conditions for a Class of Inverse Optimal Control Problems With Partial Differential Equations (SPP1962048, 01/2018, [bib])
Constantin Christof, Gerd Wachsmuth: Differential Sensitivity Analysis of Variational Inequalities with Locally Lipschitz Continuous Solution Operators (SPP1962039, 11/2017, [bib])
Constantin Christof, Gerd Wachsmuth: On the NonPolyhedricity of Sets with Upper and Lower Bounds in Dual Spaces (SPP1962031, 08/2017, [bib])
Felix Harder: Legendre Forms in Reflexive Banach Spaces (SPP1962030, 08/2017, [bib])
Felix Harder, Gerd Wachsmuth: Comparison of Optimality Systems for the Optimal Control of the Obstacle Problem (SPP1962029, 08/2017, [bib])
Constantin Christof, Gerd Wachsmuth: NoGap SecondOrder Conditions via a Directional Curvature Functional (SPP1962026, 07/2017, [bib])
Patrick Mehlitz: On the Sequential Normal Compactness Condition and its Restrictiveness in Selected Function Spaces (SPP1962025, 06/2017, [bib])
Felix Harder, Gerd Wachsmuth: The Limiting Normal Cone of a Complementarity Set in Sobolev Spaces (SPP1962023, 06/2017, [bib])
Patrick Mehlitz, Gerd Wachsmuth: The Weak Sequential Closure of Decomposable Sets in Lebesgue Spaces and its Application to Variational Geometry (SPP1962016, 04/2017, [bib])
Patrick Mehlitz, Gerd Wachsmuth: The Limiting Normal Cone to Pointwise Defined Sets in Lebesgue Spaces (SPP1962004, 12/2016, [bib])
Ulisse Stefanelli, Daniel Wachsmuth, Gerd Wachsmuth: Optimal control of a rateindependent evolution equation via viscous regularization (SPP1962001, 11/2016, [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.Members
Project Related News

Sep 09, 2019 : New preprint submitted
Gerd Wachsmuth submitted the preprint SPP1962118, Elliptic QuasiVariational Inequalities under a Smallness Assumption: Uniqueness, Differential Stability and Optimal Control

Jun 21, 2019 : New preprint submitted
Gerd Wachsmuth submitted the preprint SPP1962113, On SecondOrder Optimality Conditions for Optimal Control Problems Governed by the Obstacle Problem

Mar 26, 2019 : New publications
The preprints SPP1962048, SPP1962053, SPP1962057 and SPP1962066 have been published.

Dec 04, 2018 : New publications
Preprints SPP1962023 and SPP1962030 have been published.

Oct 26, 2018 : New preprint submitted
Gerd Wachsmuth submitted the preprint SPP1962094, Optimal Control of ODEs with State Suprema

Oct 09, 2018 : New preprint submitted
Patrick Mehlitz submitted the preprint SPP1962082, Semivectorial Bilevel Programming versus Scalar Bilevel Programming

Jun 13, 2018 : New preprint submitted
Gerd Wachsmuth submitted the Preprint SPP1962057, Generalized Derivatives for the Solution Operator of the Obstacle Problem

Feb 14, 2018 : New preprint submitted
Patrick Mehlitz submitted the Preprint SPP1962050, On an Optimal Control Problem with Gradient Constraints

Jan 27, 2018 : New preprint submitted
Felix Harder submitted the Preprint SPP1962048, Optimality Conditions for a Class of Inverse Optimal Control Problems with Partial Differential Equations

Jul 06, 2017 : New preprint submitted
Patrick Mehlitz submitted the Preprint SPP1962025, On the Sequential Normal Compactness Condition and its Restrictiveness in Selected Function Spaces