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Christian Clason: Publikationen
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 , submitted 2022; 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 .
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 ]
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 .
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.
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