@misc{SchneiderWachsmuth, author = {Schneider, Christopher and Wachsmuth, Gerd}, title = {Regularization and discretization error estimates for optimal control of ODEs with group sparsity}, series = {ESAIM: Control, Optimisation and Calculus of Variations (COCV)}, volume = {24}, journal = {ESAIM: Control, Optimisation and Calculus of Variations (COCV)}, number = {2}, issn = {1292-8119}, doi = {10.1051/cocv/2017049}, pages = {811 -- 834}, abstract = {It is well known that optimal control problems with L¹-control costs produce sparse solutions, i.e., the optimal control is zero on whole intervals. In this paper, we study a general class of convex linear-quadratic optimal control problems with a sparsity functional that promotes a so-called group sparsity structure of the optimal controls. In this case, the components of the control function take the value of zero on parts of the time interval, simultaneously. These problems are both theoretically interesting and practically relevant. After obtaining results about the structure of the optimal controls, we derive stability estimates for the solution of the problem w.r.t. perturbations and L²-regularization. These results are consequently applied to prove convergence of the Euler discretization. Finally, the usefulness of our approach is demonstrated by solving an illustrative example using a semismooth Newton method.}, language = {en} } @misc{SchneiderWachsmuth, author = {Schneider, Ren{\´e} and Wachsmuth, Gerd}, title = {Achieving optimal convergence order for FEM in control constrained optimal control problems}, series = {Proceedings in Applied Mathematics and Mechanics (PAMM)}, volume = {15}, journal = {Proceedings in Applied Mathematics and Mechanics (PAMM)}, number = {1}, issn = {1617-7061}, doi = {10.1002/pamm.201510350}, pages = {731 -- 734}, abstract = {We propose a new heuristic approach to overcome convergence order restrictions implied by the low regularity of the optimal control due to the activity interface of control constraints. Aligning the mesh with the interface yields an improved approximation of the control. Utility of the approach is demonstrated by numerical experiments.}, language = {en} } @misc{ZschechGeislerRinderknechtetal., author = {Zschech, Ehrenfried and Geisler, Holm and Rinderknecht, Jochen and Schneider, Gerd and Spolenak, Ralph and Schmeißer, Dieter}, title = {Nano-scale analysis using synchrotron-radiation: Applications in the semiconductor industry}, series = {Current nanoscience}, volume = {4}, journal = {Current nanoscience}, number = {3}, issn = {1573-4137}, pages = {256 -- 266}, language = {en} } @misc{SchneiderWachsmuth, author = {Schneider, Ren{\´e} and Wachsmuth, Gerd}, title = {A-posteriori error estimation for control-constrained, linear-quadratic optimal control problems}, series = {SIAM Journal on Numerical Analysis}, volume = {54}, journal = {SIAM Journal on Numerical Analysis}, number = {2}, issn = {1095-7170}, doi = {10.1137/15M1020460}, pages = {1169 -- 1192}, abstract = {We derive a posteriori error estimates for control-constrained, linear-quadratic optimal control problems. The error is measured in a norm which is motivated by the objective. Our abstract error estimator is separated into three contributions: the error in the variational inequality (i.e., in the optimality condition for the control) and the errors in the state and adjoint equation. Hence, one can use well-established estimators for the differential equations. We show that the abstract error estimator is reliable and efficient if the utilized estimators for the differential equations have these properties. We apply the error estimator to two distributed optimal control problems with distributed and boundary observation, respectively. Numerical examples exhibit a good error reduction if we use the local error contributions for an adaptive mesh refinement.}, language = {en} }