Projects: DFG Research Center Matheon "Mathematics for key technologies"

Lubkoll, Lars ; Schiela, Anton ; Weiser, Martin:
An affine covariant composite step method for optimization with PDEs as equality constraints.
Konrad-Zuse-Zentrum für Informationstechnik Berlin
Berlin , 2015 . - 40 p. - (ZIB-Report ; 15-09 )

Hintermüller, Michael ; Schiela, Anton ; Wollner, Winnifried:
The length of the primal-dual path in Moreau-Yosida-based path-following methods for state constrained optimal control.
In: SIAM Journal on Optimization. Vol. 24 (2014) Issue 1 . - pp. 108-126.
DOI: https://doi.org/10.1137/120866762

Review:

AMS MathSciNet Zentralblatt

Schiela, Anton ; Ulbrich, Stefan:
Operator preconditioning for a class of inequality constrained optimal control problems.
In: SIAM Journal on Optimization. Vol. 24 (2014) Issue 1 . - pp. 435-466.
DOI: https://doi.org/10.1137/120877532

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AMS MathSciNet Zentralblatt

Lubkoll, Lars ; Schiela, Anton ; Weiser, Martin:
An optimal control problem in polyconvex hyperelasticity.
In: SIAM Journal on Control and Optimization. Vol. 52 (2014) Issue 3 . - pp. 1403-1422.
DOI: https://doi.org/10.1137/120876629

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AMS MathSciNet Zentralblatt

Sander, Oliver ; Schiela, Anton:
Variational analysis of the coupling between a geometrically exact Cosserat rod and an elastic continuum.
In: Zeitschrift für angewandte Mathematik und Physik. Vol. 65 (2014) Issue 6 . - pp. 1261-1288.
DOI: https://doi.org/10.1007/s00033-013-0389-y

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AMS MathSciNet

Schiela, Anton:
A concise proof for existence and uniqueness of solutions of linear parabolic PDEs in the context of optimal control.
In: Systems & Control Letters. Vol. 62 (2013) Issue 10 . - pp. 895-901.
DOI: https://doi.org/10.1016/j.sysconle.2013.06.013

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AMS MathSciNet Zentralblatt

Schiela, Anton ; Wachsmuth, Daniel:
Convergence analysis of smoothing methods for optimal control of stationary variational inequalities with control constraints.
In: ESAIM : Mathematical Modelling and Numerical Analysis. Vol. 47 (2013) Issue 3 . - pp. 771-787.
DOI: https://doi.org/10.1051/m2an/2012049

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AMS MathSciNet Zentralblatt

Schiela, Anton:
An interior point method in function space for the efficient solution of state constrained optimal control problems.
In: Mathematical Programming Series A. Vol. 138 (2013) Issue 1-2 . - pp. 83-114.
DOI: https://doi.org/10.1007/s10107-012-0595-y

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Klapproth, Corinna ; Schiela, Anton ; Deuflhard, Peter:
Adaptive numerical integration of dynamical contact problems.
2012
Event: Thematic Conference of the European Community on Computational Methods in Applied Sciences (ECCOMAS), 2nd International Conference on Computational Contact Mechanics (ICCCM 2011) , 15.-17. Juni 2011 , Hannover, Germany.
(Conference item: Conference , Speech )

Klapproth, Corinna ; Schiela, Anton ; Deuflhard, Peter:
Fast algorithms for the simulation of human knee joint motion.
In: Proceedings of the IASTED International Conference on Biomedical Engineering (BioMed 2012), February 15-17, 2012, Innsbruck, Austria. - Anaheim, CA : ACTA Press, 2012 . - pp. 696-699
DOI: https://doi.org/10.2316/P.2012.764-176

Deuflhard, Peter ; Schiela, Anton ; Weiser, Martin:
Mathematical cancer therapy planning in deep regional hyperthermia.
In: Acta Numerica. Vol. 21 (2012) . - pp. 307-378.
DOI: https://doi.org/10.1017/S0962492912000049

Review:

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Klapproth, Corinna ; Schiela, Anton ; Deuflhard, Peter:
Adaptive timestep control for the contact-stabilized Newmark method.
In: Numerische Mathematik. Vol. 119 (2011) Issue 1 . - pp. 49-81.
DOI: https://doi.org/10.1007/s00211-011-0374-3

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Schiela, Anton ; Wollner, Winnifried:
Barrier Methods for Optimal Control Problems with Convex Nonlinear Gradient State Constraints.
In: SIAM Journal on Optimization. Vol. 21 (2011) Issue 1 . - pp. 269-286.
DOI: https://doi.org/10.1137/080742154

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AMS MathSciNet Zentralblatt

Hinze, Michael ; Schiela, Anton:
Discretization of interior point methods for state constrained elliptic optimal control problems : optimal error estimates and parameter adjustment.
In: Computational Optimization and Applications. Vol. 48 (2011) Issue 3 . - pp. 581-600.
DOI: https://doi.org/10.1007/s10589-009-9278-x

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Schiela, Anton ; Günther, Andreas:
An interior point algorithm with inexact step computation in function space for state constrained optimal control.
In: Numerische Mathematik. Vol. 119 (2011) Issue 2 . - pp. 373-407.
DOI: https://doi.org/10.1007/s00211-011-0381-4

Review:

AMS MathSciNet Zentralblatt

Meyer, Christian ; Panizzi, Lucia ; Schiela, Anton:
Uniqueness criteria for the adjoint equation in state-constrained elliptic optimal control.
In: Numerical Functional Analysis and Optimization. Vol. 32 (2011) Issue 9 . - pp. 983-1007.
DOI: https://doi.org/10.1080/01630563.2011.587074

Review:

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Schiela, Anton ; Weiser, Martin:
Barrier Methods for a Control Problem from Hyperthermia Treatment Planning.
In: Recent Advances in Optimization and its Applications in Engineering. - Berlin : Springer, 2010 . - pp. 419-428
DOI: https://doi.org/10.1007/978-3-642-12598-0_36

Klapproth, Corinna ; Schiela, Anton ; Deuflhard, Peter:
Consistency results on Newmark methods for dynamical contact problems.
In: Numerische Mathematik. Vol. 116 (2010) Issue 1 . - pp. 65-94.
DOI: https://doi.org/10.1007/s00211-010-0300-0

Review:

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Deuflhard, Peter ; Kornhuber, Ralf ; Sander, Oliver ; Schiela, Anton ; Weiser, Martin:
Mathematics cures virtual patients.
In: MATHEON - Mathematics for Key Technologies. - Zürich : European Math. Soc., 2010 . - pp. 7-25 . - (EMS Series in Industrial and Applied Mathematics ; 1 )
DOI: https://doi.org/10.4171/137

Schiela, Anton:
Barrier methods for optimal control problems with state constraints.
In: SIAM Journal on Optimization. Vol. 20 (2009) Issue 2 . - pp. 1002-1031.
DOI: https://doi.org/10.1137/070692789

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AMS MathSciNet Zentralblatt

Schiela, Anton:
An extended mathematical framework for barrier methods in function space.
In: Bercovier, Michel ; Gander, Martin J. ; Kornhuber, Ralf ; Widlund, Olof (Hrsg.): Domain decomposition methods in science and engineering XVIII. - Berlin : Springer, 2009 . - pp. 201-208 . - (Lecture Notes in Computational Science and Engineering ; 70 )
DOI: https://doi.org/10.1007/978-3-642-02677-5_21

Review:

Zentralblatt AMS MathSciNet

Haller-Dintelmann, Robert ; Meyer, Christian ; Rehberg, Joachim ; Schiela, Anton:
Hölder continuity and optimal control for nonsmooth elliptic problems.
In: Applied Mathematics and Optimization. Vol. 60 (2009) Issue 3 . - pp. 397-428.
DOI: https://doi.org/10.1007/s00245-009-9077-x

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Schiela, Anton:
Interior point methods in function space : Newton path-following and adaptivity.
In: Oberwolfach Reports. Vol. 6 (2009) Issue 04 . - pp. 254-256.
DOI: https://doi.org/10.4171/OWR/2009/04

Prüfert, Uwe ; Schiela, Anton:
The minimization of a maximum-norm functional subject to an elliptic PDE and state constraints.
In: ZAMM : Journal of Applied Mathematics and Mechanics = Zeitschrift für angewandte Mathematik und Mechanik. Vol. 89 (2009) Issue 7 . - pp. 536-551.
DOI: https://doi.org/10.1002/zamm.200800097

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Klapproth, Corinna ; Deuflhard, Peter ; Schiela, Anton:
A perturbation result for dynamical contact problems.
In: Numerical Mathematics : Theory, Methods and Applications. Vol. 2 (2009) Issue 3 . - pp. 237-257.
DOI: https://doi.org/10.4208/nmtma.2009.m9003

Review:

AMS MathSciNet Zentralblatt

Schiela, Anton:
State constrained optimal control problems with states of low regularity.
In: SIAM Journal on Control and Optimization. Vol. 48 (2009) Issue 4 . - pp. 2407-2432.
DOI: https://doi.org/10.1137/080727610

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AMS MathSciNet Zentralblatt

Weiser, Martin ; Gänzler, Tobias ; Schiela, Anton:
A control reduced primal interior point method for a class of control constrained optimal control problems.
In: Computational Optimization and Applications. Vol. 41 (2008) Issue 1 . - pp. 127-145.
DOI: https://doi.org/10.1007/s10589-007-9088-y

Review:

AMS MathSciNet Zentralblatt

Schiela, Anton:
A simplified approach to semismooth Newton methods in function space.
In: SIAM Journal on Optimization. Vol. 19 (2008) Issue 3 . - pp. 1417-1432.
DOI: https://doi.org/10.1137/060674375

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AMS MathSciNet Zentralblatt

Schiela, Anton ; Weiser, Martin:
Superlinear convergence of the control reduced interior point method for PDE constrained optimization.
In: Computational Optimization and Applications. Vol. 39 (2008) Issue 3 . - pp. 369-393.
DOI: https://doi.org/10.1007/s10589-007-9057-5

Review:

AMS MathSciNet Zentralblatt

Schiela, Anton:
A continuity result for Nemyckii Operators and some applications in PDE constrained optimal control.
Konrad-Zuse-Zentrum für Informationstechnik Berlin
Berlin , 2006 . - (ZIB-Report ; 06-41 )

Schiela, Anton:
Convergence of the Control Reduced Interior Point Method for PDE Constrained Optimal Control with State Constraints.
Konrad-Zuse-Zentrum für Informationstechnik Berlin
Berlin , 2006 . - (ZIB-Report ; 06-16 )

Weiser, Martin ; Schiela, Anton ; Deuflhard, Peter:
Asymptotic mesh independence of Newton's method revisited.
In: SIAM Journal on Numerical Analysis. Vol. 42 (2005) Issue 5 . - pp. 1830-1845.
DOI: https://doi.org/10.1137/S0036142903434047

Review:

AMS MathSciNet Zentralblatt

Weiser, Martin ; Schiela, Anton:
Function space interior point methods for PDE constrained optimization.
In: Proceedings in Applied Mathematics and Mechanics. Vol. 4 (2004) Issue 1 . - pp. 43-46.
DOI: https://doi.org/10.1002/pamm.200410011