@misc{Schiela2007, author = {Schiela, Anton}, title = {An Interior Point Method in Function Space for the Efficient Solution of State Constrained Optimal Control Problems}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10471}, number = {07-44}, year = {2007}, abstract = {We propose and analyse an interior point path-following method in function space for state constrained optimal control. Our emphasis is on proving convergence in function space and on constructing a practical path-following algorithm. In particular, the introduction of a pointwise damping step leads to a very efficient method, as verified by numerical experiments.}, language = {en} } @misc{Schiela2007, author = {Schiela, Anton}, title = {Optimality Conditions for Convex State Constrained Optimal Control Problems with Discontinuous States}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10342}, number = {07-35}, year = {2007}, abstract = {We discuss first order optimality conditions for state constrained optimal control problems. Our concern is the treatment of problems, where the solution of the state equation is not known to be continuous, as in the case of boundary control in three space dimensions or optimal control with parabolic partial differential equations. We show existence of measure valued Lagrangian multipliers, which have just enough additional regularity to be applicable to all possibly discontinuous solutions of the state equation.}, language = {en} } @misc{Schiela2008, author = {Schiela, Anton}, title = {An Extended Mathematical Framework for Barrier Methods in Function Space}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10593}, number = {08-07}, year = {2008}, abstract = {An extended mathematical framework for barrier methods for state constrained optimal control compared to [Schiela, ZIB-Report 07-07] is considered. This allows to apply the results derived there to more general classes of optimal control problems, in particular to boundary control and finite dimensional control.}, language = {en} } @article{SchielaStoeckleinWeiser2021, author = {Schiela, Anton and St{\"o}cklein, Matthias and Weiser, Martin}, title = {A primal dual projection algorithm for efficient constraint preconditioning}, volume = {43}, journal = {SIAM Journal on Scientific Computing}, number = {6}, doi = {10.1137/20M1380739}, pages = {A4095 -- A4120}, year = {2021}, abstract = {We consider a linear iterative solver for large scale linearly constrained quadratic minimization problems that arise, for example, in optimization with PDEs. By a primal-dual projection (PDP) iteration, which can be interpreted and analysed as a gradient method on a quotient space, the given problem can be solved by computing sulutions for a sequence of constrained surrogate problems, projections onto the feasible subspaces, and Lagrange multiplier updates. As a major application we consider a class of optimization problems with PDEs, where PDP can be applied together with a projected cg method using a block triangular constraint preconditioner. Numerical experiments show reliable and competitive performance for an optimal control problem in elasticity.}, language = {en} } @misc{BaumannDudaSchielaetal.2026, author = {Baumann, Felix and Duda, Georg and Schiela, Anton and Weiser, Martin}, title = {Identification of Stress in Heterogeneous Contact Models}, volume = {173}, journal = {Non-Smooth and Complementarity-Based Distributed Parameter Systems}, editor = {Hinterm{\"u}ller, Michael and Herzog, Roland and Kanzow, Christian and Ulbrich, Michael and Ulbrich, Stefan}, publisher = {Springer Nature}, year = {2026}, abstract = {We develop a heterogeneous model of the lower limb system to simulate muscle forces and stresses acting on the knee joint. The modelling of the bone dynamics leads to an index-3 DAE, which we discretize by higher order collocation methods. Furthermore, we present an elastomechanical contact knee joint model of the articular cartilage. For the solution of the contact problem we develop an efficient multigrid solver, based on an Augmented-Lagrangian relaxation of the contact constraints. We formulate the identification of joint forces and resulting stresses with respect to different knee joint models as an inverse problem based on medical gait data.}, language = {en} }