Professur Numerische Mathematik (Partielle Differentialgleichungen)






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Professur Numerische Mathematik
(Partielle Differentialgleichungen)

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Prof. Dr. Roland Herzog [ Kontakt ]

Publikationen der Arbeitsgruppe

Neuere Preprints new

Veröffentlichungen in Zeitschriften

  1. R. Herzog, G. Stadler and G. Wachsmuth
    Directional Sparsity in Optimal Control of Partial Differential Equations
    erscheint in: SIAM Journal on Control and Optimization (SICON), 2011

  2. M. Bernauer and R. Herzog
    Implementation of an X-FEM Solver for the Classical Two-Phase Stefan Problem
    erscheint in: Journal of Scientific Computing, 2011
    DOI: 10.1007/s10915-011-9543-x

  3. R. Herzog and F. Schmidt
    Weak Lower Semi-continuity of the Optimal Value Function and Applications to Worst-Case Robust Optimal Control Problems
    erscheint in: Optimization, 2011
    DOI: 10.1080/02331934.2011.603322

  4. R. Herzog, C. Meyer and G. Wachsmuth
    Integrability of Displacement and Stresses in Linear and Nonlinear Elasticity with Mixed Boundary Conditions
    Preprint SPP1253-093, 2010
    Journal of Mathematical Analysis and Applications (JMAA), 382(2), p.802-813, 2011
    DOI: 10.1016/j.jmaa.2011.04.074

  5. R. Herzog and C. Meyer
    Optimal Control of Static Plasticity with Linear Kinematic Hardening
    Preprint SPP1253-086, 2009
    WIAS-Preprint 1370, 2008
    Journal of Applied Mathematics and Mechanics (ZAMM), 91(10), p.777-794, 2011
    DOI: 10.1002/zamm.200900378

  6. R. Herzog, C. Meyer and G. Wachsmuth
    Existence and Regularity of the Plastic Multiplier in Static and Quasistatic Plasticity
    GAMM Reports, 34(1), p.39-44, 2011
    DOI: 10.1002/gamm.201110006

  7. M. Bernauer and R. Herzog
    Optimal Control of the Classical Two-Phase Stefan Problem in Level Set Formulation
    CSC Preprint 10-04, 2010
    SIAM Journal on Scientific Computing (SISC), 33(1), p.342-363, 2011
    DOI: 10.1137/100783327

  8. R. Herzog and K. Kunisch
    Algorithms for PDE-Constrained Optimization
    GAMM Reports, 33(2), p.163-176, 2010
    DOI: 10.1002/gamm.201010013

  9. R. Herzog and E. Sachs
    Preconditioned Conjugate Gradient Method for Optimal Control Problems with Control and State Constraints
    Preprint SPP1253-088, 2009
    SIAM Journal on Matrix Analysis and Applications (SIMAX), 31(5), p.2291-2317, 2010
    DOI: 10.1137/090779127
    Matlab-Code: bpcg.m (Bramble-Pasciak like conjugate gradient method) Example_CC3D.tar.gz (complete Example 4.2 from the paper)

  10. G. Wachsmuth and D. Wachsmuth
    Convergence and Regularization Results for Optimal Control Problems with Sparsity Functional
    ESAIM: Control, Optimisation and Calculus of Variations (COCV), 17, p.858-886, 2011
    DOI: 10.1051/cocv/2010027

  11. R. Griesse, N. Metla and A. Rösch
    Local Quadratic Convergence of SQP for Elliptic Optimal Control Problems with Mixed Control-State Constraints
    RICAM Report 2008-21
    Control and Cybernetics, 39(3), p.717-738, 2010

  12. M. Bernauer and R. Griesse
    A Robustification Approach in Unconstrained Quadratic Optimization
    Mathematical Programming Series A, 128(1), p.231-252, 2011
    DOI: 10.1007/s10107-009-0302-9

  13. W. Alt, R. Griesse, N. Metla and A. Rösch
    Lipschitz Stability for Elliptic Optimal Control Problems with Mixed Control-State Constraints
    Optimization, 59(6), p.833-849, 2010
    DOI: 10.1080/02331930902863749

  14. R. Griesse and K. Kunisch
    A Semismooth Newton Method for Solving Elliptic Equations with Gradient Constraints
    RICAM Report 2007-29
    ESAIM Mathematical Modelling and Numerical Analysis (M2AN), 43(2), p.209-238, 2009
    DOI: 10.1051/m2an:2008049

  15. R. Griesse and A.J. Meir
    Modeling of a Magnetohydrodynamics Free Surface Problem Arising in Czochralski Crystal Growth
    Mathematical and Computer Modelling of Dynamical Systems (MCMDS), 15(2), p.163-175, 2009
    DOI: 10.1080/13873950802551542

  16. R. Griesse, N. Metla and A. Rösch
    Convergence Analysis of the SQP Method for Nonlinear Mixed-Constrained Elliptic Optimal Control Problems
    Journal of Applied Mathematics and Mechanics (ZAMM), 88(10), p.776-792, 2008
    DOI: 10.1002/zamm.200800036

  17. R. Griesse and D. Wachsmuth
    Sensitivity Analysis and the Adjoint Update Strategy for Optimal Control Problems with Mixed Control-State Constraints
    RICAM Report 2007-33
    Computational Optimization and Applications (COAP), 44(1), p.57-81, 2009
    DOI: 10.1007/s10589-008-9181-x

  18. R. Griesse and D. Lorenz
    A Semismooth Newton Method for Tikhonov Functionals with Sparsity Constraints
    Inverse Problems, 24, 035007 (19pp), 2008
    vom Editorial Board als eines der Highlights 2008 ausgewählt
    DOI: 10.1088/0266-5611/24/3/035007
    Matlab-Code: ssn.m

  19. J.C. de los Reyes and R. Griesse
    State-Constrained Optimal Control of the Stationary Navier-Stokes Equations
    RICAM Report 2005-18
    Journal of Mathematical Analysis and Applications (JMAA), 343(1), p.257-272, 2008
    DOI: 10.1016/j.jmaa.2008.01.029

  20. R. Griesse, T. Grund and D. Wachsmuth
    Update Strategies for Perturbed Nonsmooth Equations
    RICAM Report 2006-17
    Optimization Methods and Software (OMS), 23(3), p.321-343, 2008
    DOI: 10.1080/10556780701523551

  21. R. Griesse and M. Weiser
    On the Interplay Between Interior Point Approximation and Parametric Sensitivities in Optimal Control
    RICAM Report 2005-29
    Journal of Mathematical Analysis and Applications (JMAA), 337(2), p.771-793, 2008
    DOI: 10.1016/j.jmaa.2007.03.106

  22. K. Brandes and R. Griesse
    Quantitative Stability Analysis of Optimal Solutions in PDE-Constrained Optimization
    RICAM Report 2006-26
    Journal of Computational and Applied Mathematics (JCAM), 206(2), p.809-826, 2007
    DOI: 10.1016/j.cam.2006.08.038

  23. R. Griesse and B. Vexler
    Numerical Sensitivity Analysis for the Quantity of Interest in PDE-Constrained Optimization
    RICAM Report 2005-15
    SIAM Journal on Scientific Computing (SISC), 29(1), p.22-48, 2007
    DOI: 10.1137/050637273

  24. R. Griesse and K. Kunisch
    Optimal Control for a Stationary MHD System in Velocity-Current Formulation
    RICAM Report 2005-02
    SIAM Journal on Control and Optimization (SICON), 45(5), p.1822-1845, 2006
    DOI: 10.1137/050624236

  25. A. Borzi and R. Griesse
    Distributed Optimal Control of Lambda-Omega Systems
    Journal of Numerical Mathematics (JNM), 14(1), p.17-40, 2006
    DOI: 10.1163/156939506776382120

  26. R. Griesse
    Lipschitz Stability of Solutions to Some State-Constrained Elliptic Optimal Control Problems
    Journal of Analysis and its Applications (ZAA), 25(4), p.435-455, 2006
    DOI: 10.4171/ZAA/1300

  27. R. Griesse, M. Hintermüller and M. Hinze
    Differential Stability of Control Constrained Optimal Control Problems for the Navier-Stokes Equations
    RICAM Report 2004-14
    Numerical Functional Analysis and Optimization (NFAO), 26 (7-8), p.829-850, 2005
    DOI: 10.1080/01630560500434278

  28. C. Büskens and R. Griesse
    (Computational) Parametric Sensitivity Analysis of Perturbed PDE Optimal Control Problems with State and Control Constraints
    Journal of Optimization Theory and Applications (JOTA), 131(1), p.17-35, 2006
    DOI: 10.1007/s10957-006-9122-8

  29. A. Borzi and R. Griesse
    Experiences with a Space-Time Multigrid Method for the Optimal Control of a Chemical Turbulence Model
    International Journal for Numerical Methods in Fluids (IJNMF), 47(8-9), p.879-885, 2005
    DOI: 10.1002/fld.904

  30. R. Griesse and S. Volkwein
    A Primal-Dual Active Set Strategy for Optimal Boundary Control of a Nonlinear Reaction-Diffusion System
    SIAM Journal on Control and Optimization (SICON), 44(2), p.467-494, 2005
    DOI: 10.1137/S0363012903438696

  31. R. Griesse
    Parametric Sensitivity Analysis in Optimal Control of a Reaction Diffusion System - Part I: Solution Differentiability
    Numerical Functional Analysis and Optimization (NFAO), 25(1-2), p.93-117, 2004
    DOI: 10.1081/NFA-120034120

  32. R. Griesse
    Parametric Sensitivity Analysis in Optimal Control of a Reaction Diffusion System - Part II: Practical Methods and Examples
    Optimization Methods and Software (OMS), 19(2), p.217-242, 2004
    DOI: 10.1080/10556780410001654250

  33. R. Griesse and A. Walther
    Parametric Sensitivities for Optimal Control Problems using Automatic Differentiation
    Optimal Control Applications and Methods (OCAM), 24(6), p.297-314, 2003
    DOI: 10.1002/oca.733

  34. R. Griesse and A. Walther
    Evaluating Gradients in Optimal Control - Continuous Adjoints versus Automatic Differentiation
    Journal of Optimization Theory and Applications (JOTA), 122(1), p.63-86, 2004
    DOI: 10.1023/B:JOTA.0000041731.71309.f1

Eingereichte Veröffentlichungen und Preprints

  1. D. Wachsmuth and G. Wachsmuth
    Necessary conditions for convergence rates of regularizations of optimal control problems
    Januar 2012

  2. A. Günnel, R. Herzog and E. Sachs
    A Note on Preconditioners and Scalar Products for Krylov Methods in Hilbert Space
    Juli 2011

  3. G. Wachsmuth
    Optimal Control of Quasistatic Plasticity with Linear Kinematic Hardening, Part I: Existence and Discretization in Time (extended version)
    aktualisiert November 2011

  4. G. Wachsmuth
    Optimal Control of Quasistatic Plasticity with Linear Kinematic Hardening, Part II: Regularization and Optimality Conditions (extended version)
    aktualisiert November 2011

  5. E. Casas, R. Herzog and G. Wachsmuth
    Approximation of Sparse Controls in Semilinear Equations by Piecewise Linear Functions
    Juni 2011

  6. R. Herzog, K. Kunisch and J. Sass
    Primal-Dual Methods for the Computation of Trading Regions under Proportional Transaction Costs
    April 2011

  7. D. Wachsmuth and G. Wachsmuth
    On the regularization of optimization problems with inequality constraints
    RICAM Report 2011-1
    Februar 2011

  8. R. Herzog, C. Meyer and G. Wachsmuth
    B- and Strong Stationarity for Optimal Control of Static Plasticity with Hardening
    Preprint SPP1253-114, 2011
    aktualisiert Januar 2012

  9. R. Herzog, C. Meyer and G. Wachsmuth
    C-Stationarity for Optimal Control of Static Plasticity with Linear Kinematic Hardening
    Preprint SPP1253-108, 2010
    aktualisiert Januar 2012

  10. E. Casas, R. Herzog and G. Wachsmuth
    Optimality Conditions and Error Analysis of Semilinear Elliptic Control Problems with L1 Cost Functional
    aktualisiert Mai 2011

Veröffentlichungen in Tagungsbänden

  1. E. Casas, R. Herzog and G. Wachsmuth
    Approximation of Sparse Controls in Semilinear Elliptic Equations
    in: Large-Scale Scientific Computing
    (Proceedings of the 8th International Conference Large-Scale Scientific Computing, Sozopol, Bulgaria, June 6--10, 2011)
    Volume of Lecture Notes in Computer Science, Springer, Berlin, 2011

  2. M. Bernauer, R. Herzog and K. Kunisch
    Optimal Control of the Two-Phase Stefan Problem in Level Set Formulation
    in: New Directions in Simulation, Control and Analysis for Interfaces and Free Boundaries
    Mathematisches Forschungsinstitut Oberwolfach, Report No. 07/2010, 2010

  3. R. Griesse and K. Kunisch
    A Semismooth Newton Method for Solving Elliptic Equations with Gradient Constraints
    in: Optimal Control of Coupled Systems of PDE
    Mathematisches Forschungsinstitut Oberwolfach, Report No. 13/2008, p.603-605, 2008

  4. R. Griesse, A.J. Meir and K. Kunisch
    Control Issues in Magnetohydrodynamics
    in: Control of Free Boundaries
    Mathematisches Forschungsinstitut Oberwolfach, Report No. 8/2007, p.466-469, 2007

  5. R. Griesse and A.J. Meir
    Modeling of an MHD Free Surface Problem Arising in CZ Crystal Growth
    RICAM Report 2005-30
    in: Proceedings of the 5th IMACS Symposium on Mathematical Modelling (5th MATHMOD), I. Troch, F. Breitenecker (eds)
    ARGESIM Report 30, Vienna, 2006

  6. R. Griesse and K. Kunisch
    Optimal Control in Magnetohydrodynamics
    in: Optimal Control of Coupled Systems of PDE
    Mathematisches Forschungsinstitut Oberwolfach, Report No. 18/2005, p.1011-1014, 2005

  7. R. Griesse and A. Walther
    Towards Matrix-Free AD-Based Preconditioning of KKT Systems in PDE-Constrained Optimization
    Special Issue: GAMM Annual Meeting 2005, Luxemburg
    PAMM 5(1), p.47-50, 2005

  8. R. Griesse and S. Volkwein
    Parametric Sensitivity Analysis for Optimal Boundary Control of a 3D Reaction-Diffusion System
    in: Large-Scale Nonlinear Optimization, G. Di Pillo, M. Roma (eds)
    (Proceedings of the Workshop Large Scale Nonlinear Optimization, Erice, 2004)
    Volume 83 of Nonconvex Optimization and its Applications, Springer, Berlin, 2006

  9. R. Griesse and S. Volkwein
    A Semi-Smooth Newton Method for Optimal Boundary Control of a Nonlinear Reaction-Diffusion System
    Proceedings of the Sixteenth International Symposium on Mathematical Theory of Networks and Systems (MTNS), Leuven, Belgium, 2004

  10. R. Griesse and A. Walther
    Using AD-generated Derivatives in Optimal Control of an Industrial Robot
    Progress in Industrial Mathematics at ECMI 2002, p.127-132, Springer, 2004

  11. R. Griesse
    A Reduced SQP Algorithm for the Optimal Control of Semilinear Parabolic Equations --- and its Application to Reaction-Diffusion Systems
    System Modeling and Optimization XX, Proceedings of the 20th IFIP TC 7 Conference (Trier, Germany), p.239-253, Kluwer Academic Publishers, 2003

  12. R. Griesse
    Some Aspects for Instantaneous Boundary Control of Backward-facing Step Flow
    Proceedings of the GAMM 2000 Annual Scientific Meeting, Göttingen, Germany, Zeitschrift für Angewandte Mathematik und Mechanik 81, Suppl. 2, p.251-252, 2001

Weitere Dokumente

  1. R. Herzog
    Algorithms and Preconditioning in PDE-Constrained Optimization
    erweitertes Skript zu einem Vortrag auf der Sommerschule Analysis and Numerics of PDE Constrained Optimization, Lambrecht
    Juli 2010

  2. M. Bernauer
    Motion Planning for the Two-Phase Stefan Problem in Level Set Formulation
    Dissertation, TU Chemnitz, 2010

  3. R. Griesse
    Stability and Sensitivity Analysis in Optimal Control of Partial Differential Equations
    Cumulative Habilitation Thesis, Karl Franzens University Graz, Austria, 2008

  4. G. Wachsmuth
    Elliptische Optimalsteuerungsprobleme unter Sparsity-Constraints
    Diploma Thesis, TU Chemnitz, 2008

  5. R. Griesse
    The RICAM Information Leaflet (Information for Incoming Ph.D. Students, Postdocs, and Visiting Scientists), 2005

  6. R. Griesse
    Parametric Sensitivity Analysis for Control-Constrained Optimal Control Problems Governed by Systems of Parabolic Partial Differential Equations (PDF, 22 MB)
    Dissertation, University of Bayreuth, 2003

  7. R. Griesse
    Optimale und suboptimale Steuerung der Navier-Stokes-Gleichungen
    Diploma Thesis, TU Clausthal, 1999