@misc{SchielaWachsmuth2011, author = {Schiela, Anton and Wachsmuth, Daniel}, title = {Convergence Analysis of Smoothing Methods for Optimal Control of Stationary Variational Inequalities}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-13125}, number = {11-23}, year = {2011}, abstract = {In the article an optimal control problem subject to a stationary variational inequality is investigated. The optimal control problem is complemented with pointwise control constraints. The convergence of a smoothing scheme is analyzed. There, the variational inequality is replaced by a semilinear elliptic equation. It is shown that solutions of the regularized optimal control problem converge to solutions of the original one. Passing to the limit in the optimality system of the regularized problem allows to prove C-stationarity of local solutions of the original problem. Moreover, convergence rates with respect to the regularization parameter for the error in the control are obtained. These rates coincide with rates obtained by numerical experiments, which are included in the paper.}, language = {en} } @misc{SchielaHintermueller2011, author = {Schiela, Anton and Hinterm{\"u}ller, Michael}, title = {On the Length of the Primal-Dual Path in Moreau-Yosida-based Path-following for State Constrained Optimal Control: Analysis and Numerics}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14071}, number = {11-37}, year = {2011}, abstract = {We derive a-priori estimates on the length of the primal-dual path that results from a Moreau-Yosida approximation of the feasible set for state constrained optimal control problems. These bounds depend on the regularity of the state and the dimension of the problem. Comparison with numerical results indicates that these bounds are sharp and are attained for the case of a single active point.}, language = {en} } @misc{DeuflhardSchielaWeiser2011, author = {Deuflhard, Peter and Schiela, Anton and Weiser, Martin}, title = {Mathematical Cancer Therapy Planning in Deep Regional Hyperthermia}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14204}, number = {11-39}, year = {2011}, abstract = {This paper surveys the required mathematics for a typical challenging problem from computational medicine, the cancer therapy planning in deep regional hyperthermia. In the course of many years of close cooperation with clinics, the medical problem gave rise to quite a number of subtle mathematical problems, part of which had been unsolved when the common project started. Efficiency of numerical algorithms, i.e. computational speed and monitored reliability, play a decisive role for the medical treatment. Off-the-shelf software had turned out to be not sufficient to meet the requirements of medicine. Rather, new mathematical theory as well as new numerical algorithms had to be developed. In order to make our algorithms useful in the clinical environment, new visualization software, a virtual lab, including 3D geometry processing of individual virtual patients had to be designed and implemented. Moreover, before the problems could be attacked by numerical algorithms, careful mathematical modelling had to be done. Finally, parameter identification and constrained optimization for the PDEs had to be newly analyzed and realized over the individual patient's geometry. Our new techniques had an impact on the specificity of the individual patients' treatment and on the construction of an improved hyperthermia applicator.}, language = {en} } @article{SchielaGuenther2011, author = {Schiela, Anton and G{\"u}nther, Andreas}, title = {An Interior Point Algorithm with Inexact Step Computation in Function Space for State Constrained Optimal Control}, volume = {119}, journal = {Numer. Math.}, number = {2}, publisher = {Springer Berlin / Heidelberg}, doi = {10.1007/s00211-011-0381-4}, pages = {373 -- 407}, year = {2011}, language = {en} } @article{HinzeSchiela2011, author = {Hinze, Michael and Schiela, Anton}, title = {Discretization of Interior Point Methods for State Constrained Elliptic Optimal Control Problems: optimal error estimates and parameter adjustment}, volume = {48}, journal = {Comp. Opt. and Appl.}, number = {3}, publisher = {Springer}, doi = {10.1007/s10589-009-9278-x}, pages = {581 -- 600}, year = {2011}, language = {en} }