@misc{Schiela, 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}, 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} } @misc{SchielaGuenther, author = {Schiela, Anton and G{\"u}nther, Andreas}, title = {Interior Point Methods in Function Space for State Constraints - Inexact Newton and Adaptivity}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11007}, number = {09-01}, abstract = {We consider an interior point method in function space for PDE constrained optimal control problems with state constraints. Our emphasis is on the construction and analysis of an algorithm that integrates a Newton path-following method with adaptive grid refinement. This is done in the framework of inexact Newton methods in function space, where the discretization error of each Newton step is controlled by adaptive grid refinement in the innermost loop. This allows to perform most of the required Newton steps on coarse grids, such that the overall computational time is dominated by the last few steps. For this purpose we propose an a-posteriori error estimator for a problem suited norm.}, language = {en} } @misc{PruefertSchiela, author = {Pr{\"u}fert, Uwe and Schiela, Anton}, title = {The minimization of an L^{\infty}-functional subject to an elliptic PDE and state constraints}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10714}, number = {08-17}, abstract = {We study the optimal control of a maximum-norm objective functional subject to an elliptic-type PDE and pointwise state constraints. The problem is transformed into a problem where the non-differentiable L^{\infty}-norm in the functional will be replaced by a scalar variable and additional state constraints. This problem is solved by barrier methods. We will show the existence and convergence of the central path for a class of barrier functions. Numerical experiments complete the presentation.}, language = {en} } @misc{KlapprothDeuflhardSchiela, author = {Klapproth, Corinna and Deuflhard, Peter and Schiela, Anton}, title = {A Perturbation Result for Dynamical Contact Problems}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10793}, number = {08-27}, abstract = {This paper is intended to be a first step towards the continuous dependence of dynamical contact problems on the initial data as well as the uniqueness of a solution. Moreover, it provides the basis for a proof of the convergence of popular time integration schemes as the Newmark method. We study a frictionless dynamical contact problem between both linearly elastic and viscoelastic bodies which is formulated via the Signorini contact conditions. For viscoelastic materials fulfilling the Kelvin-Voigt constitutive law, we find a characterization of the class of problems which satisfy a perturbation result in a non-trivial mix of norms in function space. This characterization is given in the form of a stability condition on the contact stresses at the contact boundaries. Furthermore, we present perturbation results for two well-established approximations of the classical Signorini condition: The Signorini condition formulated in velocities and the model of normal compliance, both satisfying even a sharper version of our stability condition.}, language = {en} } @misc{SchielaWollner, author = {Schiela, Anton and Wollner, Winnifried}, title = {Barrier Methods for Optimal Control Problems with Convex Nonlinear Gradient Constraints}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11014}, number = {08-47}, abstract = {In this paper we are concerned with the application of interior point methods in function space to gradient constrained optimal control problems, governed by partial differential equations. We will derive existence of solutions together with first order optimality conditions. Afterwards we show continuity of the central path, together with convergence rates depending on the interior point parameter.}, language = {en} } @misc{Schiela, author = {Schiela, Anton}, title = {State constrained optimal control problems with states of low regularity}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-509}, number = {08-24}, abstract = {We consider first order optimality conditions for state constrained optimal control problems. In particular we study the case where the state equation has not enough regularity to admit existence of a Slater point in function space. We overcome this difficulty by a special transformation. Under a density condition we show existence of Lagrange multipliers, which have a representation via measures and additional regularity properties.}, language = {en} } @article{SchielaWeiser2008, author = {Schiela, Anton and Weiser, Martin}, title = {Superlinear convergence of the Control Reduced Interior Point Method for PDE Constrained Optimization}, series = {Computational Optimization and Applications}, volume = {39}, journal = {Computational Optimization and Applications}, number = {3}, pages = {369 -- 393}, year = {2008}, language = {en} } @article{Schiela2008, author = {Schiela, Anton}, title = {A Simplified Approach to Semismooth Newton Methods in Function Space}, series = {SIAM J. on Optimization}, volume = {19}, journal = {SIAM J. on Optimization}, number = {3}, pages = {369 -- 393}, year = {2008}, language = {en} } @article{WeiserGaenzlerSchiela2007, author = {Weiser, Martin and G{\"a}nzler, Tobias and Schiela, Anton}, title = {A control reduced primal interior point method for a class of control constrained optimal control problems}, series = {Comput. Optim. Appl.}, volume = {41}, journal = {Comput. Optim. Appl.}, number = {1}, pages = {127 -- 145}, year = {2007}, language = {en} }