Team > Prof. Dr. Anton Schiela

Department of Mathematics
Chair of Applied Mathematics

Department of Mathematics
Chair of Applied Mathematics

• Optimal control with partial differential equations
• Newton methods in function space
• Optimization on manifolds
• Optimization in machine learning
• Applications in computational medicine
  

Department of Mathematics
Chair of Applied Mathematics

Publications

2024

Working Papers & Preprints    ↑ top

Laura Weigl and Anton Schiela: Newton's method for nonlinear mappings into vector bundles.. - Bayreuth, 2024-06-18. - 31 S.
doi:10.48550/arXiv.2404.04073

Frederik Köhne, Friedrich M. Philipp, Manuel Schaller, Anton Schiela and Karl Worthmann: L∞-error bounds for approximations of the Koopman operator by kernel extended dynamic mode decomposition.. - Ilmenau ; Bayreuth, 2024-03-28. - 21 S.
doi:10.48550/arXiv.2403.18809

2023

Articles (reviewed)    ↑ top

Bastian Pötzl, Anton Schiela and Patrick Jaap: Inexact Proximal Newton methods in Hilbert spaces. In: Computational Optimization and Applications, (2023). - S. 1-37.
doi:10.1007/s10589-023-00515-x

Working Papers & Preprints    ↑ top

Frederik Köhne, Leonie Kreis, Anton Schiela and Roland Herzog: Adaptive Step Sizes for Preconditioned Stochastic Gradient Descent.. - Bayreuth ; Heidelberg, 2023-11. - 31 S.
doi:10.48550/arXiv.2311.16956

Roland Herzog, Frederik Köhne, Leonie Kreis and Anton Schiela: Frobenius-Type Norms and Inner Products of Matrices and Linear Maps with Applications to Neural Network Training.. - Bayreuth ; Heidelberg, 2023-11. - 14 S.
doi:10.48550/arXiv.2311.15419

Evelyn Herberg, Roland Herzog, Frederik Köhne, Leonie Kreis and Anton Schiela: Sensitivity-Based Layer Insertion for Residual and Feedforward Neural Networks.. - Bayreuth ; Heidelberg, 2023-11. - 15 S.
doi:10.48550/arXiv.2311.15995

Tobias Sproll and Anton Schiela: Numerical Solution of an Identifcation Problem in Electromyography.. - Bayreuth, 2023-06. - 21 S.

2022

Articles (reviewed)    ↑ top

Lars Grüne, Manuel Schaller and Anton Schiela: Efficient Model Predictive Control for parabolic PDEs with goal oriented error estimation. In: SIAM Journal on Scientific Computing, 44 (2022). - S. A471-A500.
doi:10.1137/20M1356324

Bastian Pötzl, Anton Schiela and Patrick Jaap: Second order semi-smooth proximal Newton methods in Hilbert spaces. In: Computational Optimization and Applications, 82 (2022). - S. 465-498.
doi:10.1007/s10589-022-00369-9

2021

Articles (reviewed)    ↑ top

Tobias Sproll and Anton Schiela: An adjoint approach to identification in Electromyography : Modeling and first order optimality conditions. In: Inverse Problems, 37 (2021). - .
doi:10.1088/1361-6420/ac362c

Lars Grüne, Manuel Schaller and Anton Schiela: Abstract nonlinear sensitivity and turnpike analysis and an application to semilinear parabolic PDEs. In: ESAIM : Control, Optimisation and Calculus of Variations, 27 (2021). - .
doi:10.1051/cocv/2021030

2020

Articles (reviewed)    ↑ top

Lars Grüne, Manuel Schaller and Anton Schiela: Exponential sensitivity and turnpike analysis for linear quadratic optimal control of general evolution equations. In: Journal of Differential Equations, 268 (2020). - S. 7311-7341.
doi:10.1016/j.jde.2019.11.064

Markus Hahn, Anton Schiela, Patrick Mößle, Felix Katzer and Michael A. Danzer: Revealing inhomogeneities in electrode lithiation using a real-time discrete electro-chemical model. In: Journal of Power Sources, 477 (2020). - .
doi:10.1016/j.jpowsour.2020.228672

Working Papers & Preprints    ↑ top

Lars Grüne, Manuel Schaller and Anton Schiela: Exponential sensitivity analysis for Model Predictive Control of PDEs.. - Bayreuth, 2020-01. - 4 S.

2019

Articles (reviewed)    ↑ top

Lars Grüne, Manuel Schaller and Anton Schiela: Sensitivity Analysis of Optimal Control for a Class of Parabolic PDEs Motivated by Model Predictive Control. In: SIAM Journal on Control and Optimization, 57 (2019). - S. 2753-2774.
doi:10.1137/18M1223083

Working Papers & Preprints    ↑ top

Anton Schiela and Matthias Stöcklein: Algorithms for Optimal Control of Elastic Contact Problems with Finite Strain.. - Bayreuth, 2019-09. - 21 S.

Julián Ortiz and Anton Schiela: A composite step method for equality constrained optimization on manifolds.. - Bayreuth, 2019-03-01. - 27 S.

Anton Schiela and Julián Ortiz: Second order directional shape derivatives.. - Bayreuth, 2019-02-25. - 25 S.

2018

Articles (reviewed)    ↑ top

Tobias Sproll, Anton Schiela and Madeleine Lowery: Numerical Identification of Motor Units using an Optimal Control Approach. In: IFAC-PapersOnLine, 51 (2018). - S. 174-179.
doi:10.1016/j.ifacol.2018.03.030

Articles, Proceedings and Book Chapters (non-reviewed)    ↑ top

Lars Grüne, Manuel Schaller and Anton Schiela: Sensitivity analysis of optimal control motivated by model predictive control. In: Proceedings of the 23rd International Symposium on Mathematical Theory of Networks and Systems. - Hong Kong : 2018. - S. 93-96.

Working Papers & Preprints    ↑ top

Manuel Schaller, Anton Schiela and Matthias Stöcklein: A Composite Step Method with Inexact Step Computations for PDE Constrained Optimization.. - Bayreuth, 2018-10. - 29 S.

Anton Schiela and Matthias Stöcklein: Optimal Control of Static Contact in Finite Strain Elasticity.. - Bayreuth, 2018-10. - 28 S.

2017

Articles (reviewed)    ↑ top

Christian Clason and Anton Schiela: Optimal control of elliptic equations with positive measures. In: ESAIM : Control, Optimisation and Calculus of Variations, 23 (2017). - S. 217-240.
doi:10.1051/cocv/2015046

2016

Working Papers & Preprints    ↑ top

Georg Müller and Anton Schiela: On the Control of Time Discretized Dynamical Contact Problems.. - Bayreuth, 2016. - 35 S.

2015

Working Papers & Preprints    ↑ top

Lars Lubkoll, Anton Schiela and Martin Weiser: An affine covariant composite step method for optimization with PDEs as equality constraints.. - Berlin, 2015-03-12. - 40 S.

2014

Articles (reviewed)    ↑ top

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

Anton Schiela and Stefan Ulbrich: Operator preconditioning for a class of inequality constrained optimal control problems. In: SIAM Journal on Optimization, 24 (2014). - S. 435-466.
doi:10.1137/120877532

Lars Lubkoll, Anton Schiela and Martin Weiser: An optimal control problem in polyconvex hyperelasticity. In: SIAM Journal on Control and Optimization, 52 (2014). - S. 1403-1422.
doi:10.1137/120876629

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

Working Papers & Preprints    ↑ top

Anton Schiela: A flexible framework for cubic regularization algorithms for non-convex optimization in function space.. - Hamburg-Harburg, 2014-04-04. - 26 S.

2013

Articles (reviewed)    ↑ top

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

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

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

Articles, Proceedings and Book Chapters (non-reviewed)    ↑ top

Peter Deuflhard and Anton Schiela: Katz und Maus. In: Katja Biermann, Martin Grötschel and Brigitte Lutz-Westphal (Hrsg.): Besser als Mathe : Moderne angewandte Mathematik aus dem MATHEON zum Mitmachen. 2., aktualisierte Auflage. - Wiesbaden : Springer Fachmedien, 2013. - S. 29-40.
doi:10.1007/978-3-658-01004-1_5

2012

Articles (reviewed)    ↑ top

Peter Deuflhard, Anton Schiela and Martin Weiser: Mathematical cancer therapy planning in deep regional hyperthermia. In: Acta Numerica, 21 (2012). - S. 307-378.
doi:10.1017/S0962492912000049

Conference Proceedings (reviewed)    ↑ top

Sebastian Götschel, Martin Weiser and Anton Schiela: Solving Optimal Control Problems with the Kaskade 7 Finite Element Toolbox. In: Dedner, Andreas ; Flemisch, Bernd ; Klöfkorn, Robert (Hrsg.): Advances in DUNE : Proceedings of the DUNE User Meeting, Held in October 6th–8th 2010 in Stuttgart, Germany. - Berlin : Springer, 2012. - S. 101-112.
doi:10.1007/978-3-642-28589-9_8

Articles, Proceedings and Book Chapters (non-reviewed)    ↑ top

Corinna Klapproth, Anton Schiela and Peter Deuflhard: Fast algorithms for the simulation of human knee joint motion. In: C. Hellmich, M. H. Hamza and D. Simsik (Hrsg.): Proceedings of the IASTED International Conference on Biomedical Engineering (BioMed 2012), February 15-17, 2012, Innsbruck, Austria. - Anaheim, CA : ACTA Press, 2012. - S. 696-699.
doi:10.2316/P.2012.764-176

Conference Talks & Posters    ↑ top

Corinna Klapproth, Anton Schiela and Peter Deuflhard: Adaptive numerical integration of dynamical contact problems. - (Vortrag), Veranstaltung: 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.

2011

Articles (reviewed)    ↑ top

Corinna Klapproth, Anton Schiela and Peter Deuflhard: Adaptive timestep control for the contact-stabilized Newmark method. In: Numerische Mathematik, 119 (2011). - S. 49-81.
doi:10.1007/s00211-011-0374-3

Anton Schiela and Winnifried Wollner: Barrier Methods for Optimal Control Problems with Convex Nonlinear Gradient State Constraints. In: SIAM Journal on Optimization, 21 (2011). - S. 269-286.
doi:10.1137/080742154

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

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

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

2010

Articles (reviewed)    ↑ top

Corinna Klapproth, Anton Schiela and Peter Deuflhard: Consistency results on Newmark methods for dynamical contact problems. In: Numerische Mathematik, 116 (2010). - S. 65-94.
doi:10.1007/s00211-010-0300-0

Conference Proceedings (reviewed)    ↑ top

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

Book Chapters (reviewed)    ↑ top

Peter Deuflhard, Ralf Kornhuber, Oliver Sander, Anton Schiela and Martin Weiser: Mathematics cures virtual patients. In: MATHEON - Mathematics for Key Technologies. - Zürich : European Math. Soc., 2010. - S. 7-25.
doi:10.4171/137

2009

Articles (reviewed)    ↑ top

Anton Schiela: Barrier methods for optimal control problems with state constraints. In: SIAM Journal on Optimization, 20 (2009). - S. 1002-1031.
doi:10.1137/070692789

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

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

Uwe Prüfert and Anton Schiela: 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, 89 (2009). - S. 536-551.
doi:10.1002/zamm.200800097

Corinna Klapproth, Peter Deuflhard and Anton Schiela: A perturbation result for dynamical contact problems. In: Numerical Mathematics : Theory, Methods and Applications, 2 (2009). - S. 237-257.
doi:10.4208/nmtma.2009.m9003

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

Conference Proceedings (reviewed)    ↑ top

Anton Schiela: 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. - S. 201-208.
doi:10.1007/978-3-642-02677-5_21

2008

Articles (reviewed)    ↑ top

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

Anton Schiela: A simplified approach to semismooth Newton methods in function space. In: SIAM Journal on Optimization, 19 (2008). - S. 1417-1432.
doi:10.1137/060674375

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

2007

Working Papers & Preprints    ↑ top

Anton Schiela: Optimality Conditions for Convex State Constrained Optimal Control Problems with Discontinuous States. - Berlin, 2007. -

2006

Working Papers & Preprints    ↑ top

Anton Schiela: A continuity result for Nemyckii Operators and some applications in PDE constrained optimal control. - Berlin, 2006. -

Anton Schiela: Convergence of the Control Reduced Interior Point Method for PDE Constrained Optimal Control with State Constraints. - Berlin, 2006. -

2005

Articles (reviewed)    ↑ top

Martin Weiser, Anton Schiela and Peter Deuflhard: Asymptotic mesh independence of Newton's method revisited. In: SIAM Journal on Numerical Analysis, 42 (2005). - S. 1830-1845.
doi:10.1137/S0036142903434047

2004

Articles (reviewed)    ↑ top

Martin Weiser and Anton Schiela: Function space interior point methods for PDE constrained optimization. In: Proceedings in Applied Mathematics and Mechanics, 4 (2004). - S. 43-46.
doi:10.1002/pamm.200410011

2003

Articles (reviewed)    ↑ top

Anton Schiela and Folkmar Bornemann: Sparsing in real time simulation. In: ZAMM : Journal of Applied Mathematics and Mechanics = Zeitschrift für angewandte Mathematik und Mechanik, 83 (2003). - S. 637-647.
doi:10.1002/zamm.200310070

2000

Articles, Proceedings and Book Chapters (non-reviewed)    ↑ top

Anton Schiela and Hans Olsson: Mixed-mode integration for real-time simulation. In: Papers of the Modelica Workshop 2000. - Linköping, Sweden : Modelica Association, 2000. - S. 69-75.

Department of Mathematics
Chair of Applied Mathematics

Prof. Dr. Anton Schiela
Professor for Applied Mathematics

University of Bayreuth
Chair of Applied Mathematics
Universitätsstraße 30
95440 Bayreuth, Germany

Phone: +49 (0)921 55-3281
E-mail: anton.schiela@uni-bayreuth.de

Fax: +49 (0)921 55-5361
Room number: 3.2 O1 533
Building: NW II, main campus
Consultation hours: please contact me by email or video conference at the moment