Christian Clason: Publikationen

Bücher

Christian Clason:
Introduction to Functional Analysis,
Compact Textbooks in Mathematics. Birkhäuser Basel, 2020.
Christian Clason:
Einführung in die Funktionalanalysis,
Mathematik Kompakt. Birkhäuser Basel, 2019.

Journale

Christian Clason, Vu Huu Nhu, Arnd Rösch:
Numerical analysis of a nonsmooth quasilinear elliptic control problem: II. Finite element discretization and error estimates,
submitted 2023; arXiv:2303.03060.
Christian Clason, Vu Huu Nhu, Arnd Rösch:
Numerical analysis of a nonsmooth quasilinear elliptic control problem: I. Explicit second-order optimality conditions,
ESAIM: Mathematical Modelling and Numerical Analysis, to appear 2024; arXiv:2203.16865.
Christian Clason, Carla Tameling, Benedikt Wirth:
Convex relaxation of discrete vector-valued optimization problems,
SIAM Review 63 (2021), 783-821; arXiv:2108.10077.
[ Matlab code ]
Christian Clason, Vu Huu Nhu, Arnd Rösch:
No-gap second-order optimality conditions for optimal control of a non-smooth quasilinear elliptic equation,
ESAIM: Control, Optimisation and Calculus of Variation 27 (2021), 62; arXiv:2003.11478.
Christian Clason, Karl Kunisch, Philip Trautmann:
Optimal control of the principal coefficient in a scalar wave equation,
Applied Mathematics and Optimization 84 (2021), 2889-2921; arXiv:1912.08672.
[ Python code ]
Christian Clason, Dirk Lorenz, Hinrich Mahler, Benedikt Wirth:
Entropic regularization of continuous optimal transport problems,
Journal of Mathematical Analysis and Applications 494 (2021), 124432; arXiv:1906.01333.
Christian Clason, Vu Huu Nhu:
Bouligand-Levenberg-Marquardt iteration for a non-smooth ill-posed problem,
Electronic Transactions on Numerical Analysis 51 (2019), 274-314; arXiv:1902.10596.
[ Python code | Julia Code ]
Christian Clason, Stanislav Mazurenko, Tuomo Valkonen:
Primal-dual proximal splitting and generalized conjugation in non-smooth non-convex optimization,
Applied Mathematics and Optimization 84 (2021), 1239-1284; arXiv:1901.02746.
[ Julia code ]
Christian Clason, Vu Huu Nhu, Arnd Rösch:
Optimal control of a non-smooth quasilinear elliptic equation,
Mathematical Control and Related Fields 11 (2021), 521-554; arXiv:1810.08007.
[ Python code ]
Christian Clason, Yu Deng, Patrick Mehlitz, Uwe Prüfert:
Optimal control problems with control complementarity constraints,
Optimization Methods and Software 35 (2020), 142-170; arXiv:1809.09920.
Christian Clason, Tapio Helin, Remo Kretschmann, Petteri Piiroinen:
Generalized modes in Bayesian inverse problems,
SIAM/ASA Journal on Uncertainty Quantification 7 (2019), 652–684; arXiv:1806.00519.
Christian Clason, Andrej Klassen:
Quasi-solution of linear inverse problems in non-reflexive Banach spaces,
Journal of Inverse and Ill-posed Problems 26 (2018), 689–702; arXiv:1803.10168.
Christian Clason, Thi Bich Tram Do, Frank Pörner:
Error estimates for the approximation of multibang control problems,
Computational Optimization and Applications 71 (2018), 857-878; arXiv:1803.04298.
[ Python code ]
Christian Clason, Vu Huu Nhu:
Bouligand-Landweber iteration for a non-smooth ill-posed problem,
Numerische Mathematik 142 (2019), 789–832; arXiv:1803.02290.
[ Python code | Julia Code ]
Christian Clason, Stanislav Mazurenko, Tuomo Valkonen:
Acceleration and global convergence of a first-order primal-dual method for nonconvex problems,
SIAM Journal on Optimization 29 (2019), 933-963; arXiv:1802.03347.
Christian Clason, Akhtar A. Khan, Miguel Sama, Christiane Tammer:
Contingent derivatives and regularization for noncoercive inverse problems,
Optimization 68 (2019), 1337-1364; arXiv:1802.05062.
Christian Clason, Florian Kruse, Karl Kunisch:
Total variation regularization of multi-material topology optimization,
ESAIM: Mathematical Modelling and Numerical Analysis 52 (2018), 275-303; arXiv:1708.06165.
Constantin Christof, Christian Clason, Christian Meyer, Stephan Walther:
Optimal control of a non-smooth semilinear elliptic equation,
Mathematical Control and Related Fields 8 (2018), 247-276; arXiv:1705.00939.
Christian Clason, Carla Tameling, Benedikt Wirth:
Vector-valued multibang control of differential equations,
SIAM Journal on Control and Optimization 56 (2018), 2295-2326; arXiv:1611.07853.
[ Matlab code ]
Richard C. Barnard, Christian Clason:
L¹ penalization of volumetric dose objectives in optimal control of PDEs,
Computational Optimization and Applications 67 (2017), 401-419; arXiv:1607.01655.
[ Python code ]
Christian Clason, Tuomo Valkonen:
Primal-dual extragradient methods for nonlinear nonsmooth PDE-constrained optimization,
SIAM Journal on Optimization 27 (2017), 1314-1339; arXiv:1606.06219.
[ Matlab code ]
Christian Clason, Karl Kunisch, Armin Rund:
Nonconvex penalization of switching control of partial differential equations,
Systems & Control Letters 106C (2017), 1-8; arXiv:1605.09750.
[ Matlab code ]
Christian Clason, Tuomo Valkonen:
Stability of saddle points via explicit coderivatives of pointwise subdifferentials,
Set-Valued and Variational Analysis 25 (2017), 69-112; arXiv:1509.06582.
Christian Clason, Barbara Kaltenbacher, Daniel Wachsmuth:
Functional error estimators for the adaptive discretization of inverse problems,
Inverse Problems 32 (2016), 104004; arXiv:1507.08077.
Christian Clason, Karl Kunisch:
A convex analysis approach to multi-material topology optimization,
ESAIM: Mathematical Modelling and Numerical Analysis 50 (2016), 1917-1936; arxiv:1702.07525.
[ Matlab code ]
Christian Clason, Armin Rund, Karl Kunisch, Richard C. Barnard:
A convex penalty for switching control of partial differential equations,
Systems & Control Letters 89 (2016), 66-73; arxiv:1702.07505.
[ Matlab code ]
Christian Clason, Anton Schiela:
Optimal control of elliptic equations with positive measures,
ESAIM: Control, Optimisation and Calculus of Variations 23 (2017), 217-240; arxiv:1702.07528.
[ Matlab code ]
Christoph Aigner, Christian Clason, Armin Rund, Rudolf Stollberger:
Efficient high-resolution RF pulse design applied to simultaneous multi-slice excitation,
Journal of Magnetic Resonance 263 (2016), 33-44; arxiv:1702.07503.
[ Matlab code ]
Christian Clason, Kazufumi Ito, Karl Kunisch:
A convex analysis approach to optimal controls with switching structure for partial differential equations,
ESAIM: Control, Optimisation and Calculus of Variations 22 (2016), 581-609; arxiv:1702.07540.
[ Matlab code ]
Christian Clason, Karl Kunisch:
Multi-bang control of elliptic systems,
Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire 31 (2014), 1109-1130.
[ Matlab code | Python code ]
Christian Clason, Barbara Kaltenbacher:
Avoiding degeneracy in the Westervelt equation by state constrained optimal control,
Evolution Equations and Control Theory 2 (2013), 281-300.
Christian Clason, Barbara Kaltenbacher:
Optimal control of a singular PDE modeling transient MEMS with control or state constraints,
Journal of Mathematical Analysis and Applications 410 (2014), 455-468.
Patricia Brunner, Christian Clason, Manuel Freiberger, Hermann Scharfetter:
A deterministic approach to the adapted optode placement for illumination of highly scattering tissue,
Biomedical Optics Express 3 (2012), 1732-1743.
Eduardo Casas, Christian Clason, Karl Kunisch:
Parabolic control problems in measure spaces with sparse solutions,
SIAM J. Control Optim. 51 (2013), 28-63.
[ Matlab code | Python code ]
Christian Clason:
L-infinity fitting for inverse problems with uniform noise,
Inverse Problems 28 (2012), 104007.
[ Matlab code | Python code ]
Christian Clason, Barbara Kaltenbacher:
On the use of state constraints in optimal control of singular PDEs,
Systems & Control Letters, 62 (2013), 48-54.
Eduardo Casas, Christian Clason, Karl Kunisch:
Approximation of elliptic control problems in measure spaces with sparse solutions,
SIAM J. Control Optim. 50 (2012), 1735-1752.
[ Matlab code | Python code ]
Christian Clason, Gregory von Winckel:
A general spectral method for the numerical simulation of one-dimensional interacting fermions,
Computer Physics Communications 183 (2011), 405-417,
Computer Physics Communications 183 (2012), 1843-1844 (new version announcement).
[ Matlab code | Python code ], published in the CPC Program Library.
Christian Clason, Karl Kunisch:
A measure space approach to optimal source placement,
Computational Optimization and Applications 53 (2012), 155-171.
[ Matlab code ]
Christian Clason, Kazufumi Ito, Karl Kunisch:
A minimum effort optimal control problem for elliptic PDEs,
ESAIM: Mathematical Modelling and Numerical Analysis 46 (2012), 911-927.
[ Matlab code ]
Florian Knoll, Christian Clason, Kristian Bredies, Martin Uecker, Rudolf Stollberger:
Parallel imaging with nonlinear reconstruction using variational penalties,
Magnetic Resonance in Medicine 67 (2012), 34-41.
Selected for the Virtual Issue: Data Sampling and Image Reconstruction.
[ Matlab code ]
Christian Clason, Bangti Jin:
A semi-smooth Newton method for nonlinear parameter identification problems with impulsive noise,
SIAM J. Imaging Sci. 5 (2012), 505-538.
[ Matlab code ]
Christian Clason, Kazufumi Ito, Karl Kunisch:
Minimal invasion: An optimal L^infty state constraint problem,
ESAIM: Mathematical Modelling and Numerical Analysis 45 (2010), 505-522.
[ Matlab code ]
Manuel Freiberger, Christian Clason, Hermann Scharfetter:
Total variation regularization for nonlinear fluorescence tomography with an augmented Lagrangian splitting approach,
Applied Optics 49 (2010), 3741-3747.
Selected for Virtual Journal for Biomedical Optics, Volume 5, Issue 11.
Christian Clason, Bangti Jin, Karl Kunisch:
A duality-based splitting method for l1-TV image restoration with automatic regularization parameter choice,
SIAM J. Sci. Comp. 32 (2010), 1484-1505.
[ Matlab code ]
Florian Knoll, Markus Unger, Christian Clason, Clemens Diwoky, Thomas Pock, Rudolf Stollberger:
Fast reduction of undersampling artifacts in radial MR angiography with 3D total variation on graphics hardware,
Magn Reson Mater Phy 23 (2010), 103-114.
Christian Clason, Bangti Jin, Karl Kunisch:
A semismooth Newton method for L1 data fitting with automatic choice of regularization parameters and noise calibration,
SIAM J. Imaging Sci. 3 (2010), 199-231.
[ Matlab code ]
Manuel Freiberger, Christian Clason, Hermann Scharfetter:
Adaptation and focusing of optode configurations for fluorescence optical tomography by experimental design methods,
Journal of Biomedical Optics 15 (2010), 016024.
Florian Knoll, Christian Clason, Clemens Diwoky, Rudolf Stollberger:
Adapted random sampling patterns for accelerated MRI,
Magn Reson Mater Phy, 24 (2011), 43-50.
Christian Clason, Karl Kunisch:
A duality-based approach to elliptic control problems in non-reflexive Banach spaces,
ESAIM: Control, Optimisation and Calculus of Variations, 17 (2011), 243-266.
[ Matlab code ]
Christian Clason, Peter Hepperger:
A forward approach to numerical data assimilation,
SIAM J. Sci. Comp. 31 (2009), 3090-3115.
Frank Bauer, Christian Clason:
On theoretical limits in parallel magnetic resonance imaging,
International Journal of Tomography & Simulation 18 (2011), 10-23.
Stephen Keeling, Christian Clason, Michael Hintermüller, Florian Knoll, Antoine Laurain, Gregory von Winckel:
An image space approach to Cartesian based parallel MR imaging with total variation regularization,
Medical Image Analysis 16 (2012), 189-200.
Christian Clason, Barbara Kaltenbacher, Slobodan Veljović:
Boundary optimal control of the Westervelt and the Kuznetsov equation,
J. Math. Anal. Appl. 356 (2009), 738-751.
Christian Clason, Gregory von Winckel:
On a bilinear optimization problem in parallel magnetic resonance imaging,
Applied Mathematics and Computation 216 (2010), 1443-1452.
Christian Clason, Michael Klibanov:
The quasi-reversibility method for thermoacoustic tomography in a heterogeneous medium,
SIAM J. Sci. Comp. 30 (2007), 1-23.
Larisa Beilina, Christian Clason:
An adaptive hybrid FEM/FDM method for an inverse scattering problem in scanning acoustic microscopy,
SIAM J. Sci. Comp. 28 (2006), 382-402.
Christian Clason, Andreas M. Hinz, Heinrich Schieferstein:
A method for material parameter determination for the human mandible based on simulation and experiment,
Comput. Methods Biomech. Biomed. Engin. 7 (2004), 265-276.

Buchkapitel

Christian Clason, Barbara Kaltenbacher, Elena Resmerita:
Regularization of ill-posed problems with non-negative solutions,
Splitting Algorithms, Modern Operator Theory, and Applications, H. Bauschke, R. Burachik, R. Luke (eds.), Springer, 2019;arXiv:1805.01722.
Christian Clason, Thi Bich Tram Do:
Convex regularization of discrete-valued inverse problems,
New Trends in Parameter Identification for Mathematical Models, B. Hofmann, A. Leitão, and J. Zubelli (eds.), Birkhäuser, 2018; arXiv:1707.01041.
[ Matlab code ]

Tagungsbeiträge

Christian Clason, Yu Deng, Patrick Mehlitz, Uwe Prüfert:
A penalization scheme for the numerical solution of optimal control problems with control complementarity constraints,
Proc. Appl. Math. Mech., 19 (2019), e201900122.
Christoph Brauer, Christian Clason, Dirk Lorenz, Benedikt Wirth:
A Sinkhorn-Newton method for entropic optimal transport,
revised 2018; arXiv:1710.06635.
[ Matlab code ]
Christoph Aigner, Christian Clason, Armin Rund, Andreas Petrovic, Rudolf Stollberger:
Design of complex RF pulse shapes for asymmetric excitation patterns via optimal control,
Biomed Tech 61, S1 (2016), S140.
Markus Bödenler, Christoph Aigner, Armin Rund, Christian Clason, Rudolf Stollberger:
Fast optimization of RF excitation,
Magn Reson Mater Phy, 29, S1 (2016), 358.
Christoph Aigner, Christian Clason, Armin Rund, Rudolf Stollberger:
Low SAR RF-pulse design by joint optimization of RF and gradient shape with physical constraints,
Proceedings of the 24th Scientific Meeting and Exhibition of ISMRM, Singapur, 7-13 May 2016, 1133.
Christian Clason, Karl Kunisch, Armin Rund:
Optimal control of partial differential equations with nonsmooth cost functionals,
Proceedings of the XXIV Congress on Differential equations and applications, Cádiz, June 8--12, 2015, 3-8.
Christoph Aigner, Christian Clason, Armin Rund, Rudolf Stollberger:
SAR reduced excitation by joint design of RF pulse and slice selective gradient shape,
Proceedings of the 23rd Scientific Meeting and Exhibition of ISMRM, Toronto, Canada, 30 May-5 June 2015, 2397.
Christoph Aigner, Christian Clason, Armin Rund, Rudolf Stollberger:
RF pulse design for simultaneous multislice excitation with highly reduced B1 peak amplitude,
Proceedings of the 23rd Scientific Meeting and Exhibition of ISMRM, Toronto, Canada, 30 May-5 June 2015, 915; oral presentation, magna cum laude award.
Christoph Aigner, Christian Clason, Armin Rund, Rudolf Stollberger:
RF pulse design for low SAR simultaneous multislice (SMS) excitation using optimal control,
Proceedings of the 22nd Scientific Meeting and Exhibition of ISMRM, Milan, Italy, 10-16 May 2014.
Christoph Aigner, Christian Clason, Armin Rund, Rudolf Stollberger:
Validation of a flexible optimal control approach for RF-pulse design including relaxation effects and SAR,
Tagungsband zur ÖGBMT-Jahrestagung 2014, 23-24.
Florian Knoll, Christian Clason, Kristian Bredies, Rudolf Stollberger:
Iterative image reconstruction for accelerated MR-imaging: Mathematics meets radiology,
Abstracts of the 29th Annual Meeting of the Austrian Society for Radio Oncology, Radio Biology and Medical Radiophysics, Gmunden, Austria, 28-29 September, 2012,
Strahlenther Onkol 189 (2013), 184-185.
Christian Clason:
Parameter identification problems with non-Gaussian noise.
in: Habib Ammari, Liliana Borcea, Thorsten Hohage, Barbara Kaltenbacher (eds.), Computational Inverse Problems,
Oberwolfach Report 9 (2013), 3117-3118.
Florian Knoll, Christian Clason, Kristian Bredies, Martin Uecker, Rudolf Stollberger:
Parallel Imaging with Nonlinear Reconstruction Using Variational Penalties,
Proceedings of the 19th Scientific Meeting and Exhibition of ISMRM, Montréal, Canada, 7-13 May 2011; oral presentation.
Markus Kraiger, Florian Knoll, Christian Clason, Rudolf Stollberger:
Assessment of Iterative Regularized Parallel Imaging Reconstruction for Quantitative Magnetic Resonance Imaging,
Proceedings of the 44th Annual Meeting of the German-Austrian-Swiss Society for Biomedical Engineering, Rostock, Germany, 5-8 October, 2010,
Biomed Tech 55:s1 (2010), 234-237.
Christian Clason, Barbara Kaltenbacher, Irena Lasiecka, Slobodan Veljović:
Optimal boundary control for equations of nonlinear acoustics,
15th International Conference on Methods and Models in Automation and Robotics (MMAR), Miedzyzdroje, Poland, 23-26 August, 2010.
Florian Knoll, Christian Clason, Rudolf Stollberger:
Tailored 3D Random Sampling Patterns for Nonlinear Parallel Imaging,
Proceedings of the 18th Scientific Meeting and Exhibition of ISMRM, Stockholm, Sweden, 1-7 May 2010.
Florian Knoll, Christian Clason, Manuela Aschauer, Franz Ebner, Rudolf Stollberger:
Adapted Random 3D Sampling Patterns for CE-MRA,
Proceedings of the 18th Scientific Meeting and Exhibition of ISMRM, Stockholm, Sweden, 1-7 May 2010.
Markus Kraiger, Florian Knoll, Christian Clason, Rudolf Stollberger:
Quantification of Transversal Relaxation Time T2 using an Iterative Regularized Parallel Imaging Reconstruction,
Proceedings of the 18th Scientific Meeting and Exhibition of ISMRM, Stockholm, Sweden, 1-7 May 2010.
Gerald Buchgraber, Florian Knoll, Manuel Freiberger, Christian Clason, Markus Grabner, Rudolf Stollberger:
Fast Regridding using LSQR on Graphics Hardware,
Proceedings of the 18th Scientific Meeting and Exhibition of ISMRM, Stockholm, Sweden, 1-7 May 2010.
Florian Knoll, Christian Clason, Franz Ebner, Manuela Aschauer, Rudolf Stollberger:
CE-MRA with tailored 3D random sampling patterns and nonlinear parallel imaging reconstruction,
21th Annual International Conference on Magnetic Resonance Angiography, East Lansing, Michigan, USA, 29 September-1 October 2009.
Florian Knoll, Christian Clason, Martin Uecker, Rudolf Stollberger:
Improved Reconstruction in non Cartesian Parallel Imaging by Regularized Nonlinear Inversion,
Proceedings of the 17th Scientific Meeting and Exhibition of ISMRM, Honolulu, Hawaii, USA, 18-24 April 2009.
Ruxandra Lasowski, Selim Benhimane, Jakob Vogel, Christian Clason, Tobias F. Jakobs, Christoph J. Zech, Christoph Trumm, Nassir Navab:
Adaptive visualization for needle guidance in RF Liver Ablation: taking organ deformation into account,
SPIE Medical Imaging, San Diego, California, USA, 16-21 February 2008.
Larisa Beilina, Christian Clason:
An inverse medium problem for scanning acoustic microscopy,
PAMM 5 (2005), 647-648.
Andreas Hinz, Christian Clason:
Quantitative sonography for bone material,
ESAIM Proc. 12 (2002), 73-74.
Christian Clason, Andreas Hinz:
Simulation of the Elastic Behaviour of the Human Mandible: Experimental Validation and Material Parameter Identification,
ESAIM Proc. 12 (2002), 31-33.
Heinrich Schieferstein et al.:
Structure Analysis of the Human Mandible -- Experimental Study and Numerical Simulation,
1st International Congress on Mastication and Health, Yokohama, September 15-18, 2002.
Heinrich Schieferstein et al.:
Experimental study and numerical simulation of the mechanical behaviour of the human mandible,
Proceedings of the XVIIIth Congress of the International Society of Biomechanics, Zürich, 2001.

Prüfungsschriften

Cumulative habilitation thesis:
Numerical solution of optimal control and inverse problems in non-reflexive Banach spaces,
Institute for Mathematics and Scientific Computing, Karl-Franzens-Universität Graz, 2012.
[ Summary ]
Dissertation:
A direct method for the numerical time reversal of waves in a heterogeneous medium,
Center for Mathematics, Technische Universität München, 2006.
Diploma thesis:
Lösung eines inversen Problems aus der Biomechanik via Finite Elemente,
Department of Mathematics, Ludwig-Maximilians-Universität München, 2001.

Andere

Christian Clason:
Preface to special issue on “Optimal Control of Nonlinear Differential Equations”
Computational Optimization and Applications, 87:i–iv, 2024.
Eduardo Casas, Christian Clason, Arnd Rösch:
System modeling and optimization (special issue preface)
Mathematical Control & Related Fields, 11(3):i–ii, 2021.
Christian Clason, Barbara Kaltenbacher:
Optimal control and inverse problems (special issue preface)
Inverse Problems, 36(6):060301, 2020.
Christian Clason, Tuomo Valkonen:
Introduction to Nonsmooth Analysis and Optimization,
work in progress, 2020; arXiv:2001.00216v4.
Christian Clason:
Regularization of Inverse Problems,
lecture notes, 2020; arXiv:2001.00617.
Christian Clason:
Optimierung mit "Knick",
UNIKATE 53 (2019), 60-67.
Christian Clason:
Introduction to Finite Element Methods,
lecture notes, 2017; arXiv:1709.08618.
Christian Clason:
Nonsmooth Analysis and Optimization,
lecture notes, 2017; arXiv:1708.04180.
Karl Kunisch, Kristian Bredies, Christian Clason, Gregory von Winckel (eds.):
Control and Optimization with PDE Constraints,
volume 164 of International Series of Numerical Mathematics, Birkhäuser, Basel, 2013.
Christian Clason, Maxim Shishlenin:
Recent advances in analytical and numerical methods in inverse problems for PDEs (minisymposium report),
J. Inverse Ill-posed Problems 18 (2011), 955-958.
Christian Clason, Andreas Hinz:
From bits to bites: mathematical simulations for cranio-maxillofacial surgery,
in Bubbles, Jaws, Moose Tests, and More: The Wonderful World of Numerical Simulation, Hans-Joachim Bungartz, Ralf-Peter Mundani, Anton Christian Frank (eds.), Springer VideoMATH, 2005.