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Research Group Numerical Mathematics (Partial Differential Equations)
Publications

Publications of the research group

Submitted Publications and Preprints

Publications in Journals

  1. R. Bergmann, R. Herzog, M. Louzeiro, D. Tenbrinck and J. Vidal-Núñez
    Fenchel Duality Theory and a Primal-Dual Algorithm on Riemannian Manifolds
    arXiv:1908.02022
    to appear in: Foundations of Computational Mathematics
    November 2020
  2. J. Blechschmidt, R. Herzog and M. Winkler
    Error estimation for second-order PDEs in non-variational form
    arXiv:1909.12676
    Numerical Methods for Partial Differential Equations, 2020
    DOI: 10.1002/num.22678
  3. M.D. Fajardo-Gomez, S.M. Grad and J. Vidal-Núñez
    New duality results for evenly convex optimization problems
    arXiv:1904.10478
    Optimization, 2020
    DOI: 10.1080/02331934.2020.1756287
  4. T. Etling, R. Herzog, E. Loayza and G. Wachsmuth
    First and Second Order Shape Optimization based on Restricted Mesh Deformations
    arXiv:1810.10313
    SIAM Journal on Scientific Computing (SISC), 42, p.A1200-A1225, 2019
    DOI: 10.1137/19M1241465
  5. J. Görthofer, M. Schneider, F. Ospald, A. Hrymak and T. Böhlke
    Computational homogenization of sheet molding compound composites based on high fidelity representative volume elements
    Computational Materials Science (CMS), 174, p.109456, 2020
    DOI: 10.1016/j.commatsci.2019.109456
  6. M. Winkler
    Error estimates for the finite element approximation of bilinear boundary control problems
    arXiv:1901.03612
    Computational Optimization and Applications (COAP), 76(1), p.155-199, 2020
    DOI: 10.1007/s10589-020-00171-5
  7. R. Bergmann, M. Herrmann, R. Herzog, S. Schmidt and J. Vidal-Núñez
    Discrete Total Variation of the Normal Vector Field as Shape Prior with Applications in Geometric Inverse Problems
    arXiv:1908.07916
    Inverse Problems (IP), 36(5), p.054004, 2020
    DOI: 10.1088/1361-6420/ab6d5c
  8. R. Bergmann, M. Herrmann, R. Herzog, S. Schmidt and J. Vidal-Núñez
    Total Variation of the Normal Vector Field as Shape Prior
    arXiv:1902.07240
    Inverse Problems (IP), 36(5), p.054003, 2020
    DOI: 10.1088/1361-6420/ab6d5b
  9. J. Hart, B. van Bloemen Waanders and R. Herzog
    Hyper-Differential Sensitivity Analysis of Uncertain Parameters in PDE-Constrained Optimization
    arXiv:1909.07336
    International Journal for Uncertainty Quantification (IJUQ), 10(3), p.225-248, 2020
    DOI: 10.1615/int.j.uncertaintyquantification.2020032480
  10. O. Ferreira, M. Louzeiro and L. Prudente
    Iteration-complexity and asymptotic analysis of steepest descent method for multiobjective optimization on Riemannian manifolds
    arXiv:1906.05975
    Journal of Optimization Theory and Applications (JOTA), 184(2), p.507-533, 2019
    DOI: 10.1007/s10957-019-01615-7
  11. M. Winkler
    Error estimates for variational normal derivatives and Dirichlet control problems with energy regularization
    arXiv:1808.01171
    Numerische Mathematik, 144, p.413–445, 2020
    DOI: 10.1007/s00211-019-01091-1
  12. O. Ferreira, M. Louzeiro and L. Prudente
    Gradient method for optimization on Riemannian manifolds with lower bounded curvature
    SIAM Journal on Optimization (SIOPT), 29(4), p.2517-2541, 2019
    DOI: 10.1137/18M1180633
  13. G. Bento, S. Bitar, J. da Cruz Neto, A. Soubeyran and J. Souza
    A proximal point method for difference of convex functions in multi-objective optimization with application to group dynamic problems
    Computational Optimization and Applications (COAP), 75(1), p.263-290, 2019
    DOI: 10.1007/s10589-019-00139-0
  14. G. Bento, S. Bitar, J. da Cruz Neto, P. Oliveira and J. Souza
    Computing Riemannian Center of Mass on Hadamard Manifolds
    Journal of Optimization Theory and Applications (JOTA), 183(3), p.977-992, 2019
    DOI: 10.1007/s10957-019-01580-1
  15. E. Batista, G. Bento and O. Ferreira
    An extragradient-type algorithm for variational inequality on Hadamard manifolds
    arXiv:1804.09292
    ESAIM: Control, Optimisation and Calculus of Variations (COCV), 26, 2020
    DOI: 10.1051/cocv/2019040
  16. J. Pfefferer and M. Winkler
    Finite element error estimates for normal derivatives on boundary concentrated meshes
    arXiv:1804.05723
    SIAM Journal on Numerical Analysis (SINUM), 57(5), p.2043-2073, 2019
    DOI: 10.1137/18M1181341
  17. T. Etling, R. Herzog and M. Siebenborn
    Optimum Experimental Design for Interface Identification Problems
    arXiv:1808.05776
    SIAM Journal on Scientific Computing (SISC), 41(6), p.A3498-A3523, 2019
    DOI: 10.1137/18M1208125
  18. R. Bergmann and R. Herzog
    Intrinsic formulation of KKT conditions and constraint qualifications on smooth manifolds
    arXiv:1804.06214
    SIAM Journal on Optimization (SIOPT), 29(4), p.2423-2444, 2019
    DOI: 10.1137/18M1181602
  19. J.C. De los Reyes and E. Loayza
    Total Generalized Variation Regularization in Variational Data Assimilation for Burgers' Equation
    arXiv:1804.04447
    Inverse Problems & Imaging (IPI), 13(4), p.755-786, 2019
    DOI: 10.3934/ipi.2019035
  20. Ospald, Felix
    fibergen: An introductory tool for FFT-based material homogenization
    Journal of Open Source Software (JOSS), 4(34), p.1027, 2019
    DOI: 10.21105/joss.01027
  21. C. Christof and G. Wachsmuth
    Differential Sensitivity Analysis of Variational Inequalities with Locally Lipschitz Continuous Solution Operators
    arXiv:1711.02720
    Applied Mathematics & Optimization (AMO), 81(1), p.23-62, 2019
    DOI: 10.1007/s00245-018-09553-y
    Preprint SPP1962-039
  22. R. Bergmann and P.-Y. Gousenbourger
    A variational model for data fitting on manifolds by minimizing the acceleration of a Bézier curve
    arXiv:1807.10090
    Frontiers in Applied Mathematics and Statistics, 4, 2018
    DOI: 10.3389/fams.2018.00059
  23. E. Casas, D. Wachsmuth and G. Wachsmuth
    Second-Order Analysis and Numerical Approximation for Bang-Bang Bilinear Control Problems
    arXiv:1707.06880
    SIAM Journal on Control and Optimization (SICON), 56(6), p.4203-4227, 2018
    DOI: 10.1137/17m1139953
  24. F. Harder and G. Wachsmuth
    Optimality conditions for a class of inverse optimal control problems with partial differential equations
    Optimization, 68(2-3), p.615-643, 2018
    DOI: 10.1080/02331934.2018.1495205
    Preprint SPP1962-048
  25. F. Harder
    Legendre forms in reflexive Banach spaces
    Zeitschrift für Analysis und ihre Anwendungen (ZAA), 37(4), p.377-388, 2018
    DOI: 10.4171/zaa/1619
    Preprint SPP1962-030
  26. F. Harder and G. Wachsmuth
    The limiting normal cone of a complementarity set in Sobolev spaces
    Optimization, 67(5), p.1579-1603, 2018
    DOI: 10.1080/02331934.2018.1484467
    Preprint SPP1962-023
  27. M. Herrmann, R. Herzog, S. Schmidt, J. Vidal-Núñez and G. Wachsmuth
    Discrete Total Variation with Finite Elements and Applications to Imaging
    arXiv:1804.07477
    Journal of Mathematical Imaging and Vision (JMIV), 61(4), p.411-431, 2019
    DOI: 10.1007/s10851-018-0852-7
  28. Th. Apel, J. Pfefferer, S. Rogovs and M. Winkler
    Maximum norm error estimates for Neumann boundary value problems on graded meshes
    arXiv:1804.10904
    IMA Journal of Numerical Analysis (IMA J. Numer. Anal.), 40(1), p.474–497, 2020
    DOI: 10.1093/imanum/dry076
  29. R. Herzog, J.W. Pearson and M. Stoll
    Fast iterative solvers for an optimal transport problem
    arXiv:1801.04172
    Advances in Computational Mathematics (ACOM), 45(2), p.495-517, 2019
    DOI: 10.1007/s10444-018-9625-5
  30. R. Herzog, I. Riedel and D. Uciński
    Optimal Sensor Placement for Joint Parameter and State Estimation Problems in Large-Scale Dynamical Systems with Applications to Thermo-Mechanics
    Optimization and Engineering (OPTE), 19(3), p.591-626, 2018
    DOI: 10.1007/s11081-018-9391-8
  31. Kimmerle, Sven-Joachim, Gerdts, Matthias and Herzog, Roland
    An Optimal Control Problem for a Rotating Elastic Crane-Trolley-Load System
    IFAC Papers Online (IFAC), 51(2), p.272-277, 2018
    DOI: 10.1016/j.ifacol.2018.03.047
  32. R. Herzog and A. Stötzner
    Hadamard Differentiability of the Solution Map in Thermoviscoplasticity
    Pure and Applied Functional Analysis (PAFA), 4(2), p.271-295, 2019
    Preprint SPP1962-044
  33. J. Köbler, M. Schneider, F. Ospald, H. Andrä and R. Müller
    Fiber orientation interpolation for the multiscale analysis of short fiber reinforced composite parts
    Computational Mechanics (CM), 61(6), p.729-750, 2018
    DOI: 10.1007/s00466-017-1478-0
  34. C. Christof and G. Wachsmuth
    No-Gap Second-Order Conditions via a Directional Curvature Functional
    arXiv:1707.07579
    SIAM Journal on Optimization (SIOPT), 28(3), p.2097-2130, 2018
    DOI: 10.1137/17M1140418
    Preprint SPP1962-026
  35. P. Benner, R. Herzog, N. Lang, I. Riedel and J. Saak
    Comparison of Model Order Reduction Methods for Optimal Sensor Placement for Thermo-Elastic Models
    Engineering Optimization, 51(3), p.465-483, 2018
    DOI: 10.1080/0305215X.2018.1469133
  36. C. Christof and G. Wachsmuth
    On the Non-Polyhedricity of Sets with Upper and Lower Bounds in Dual Spaces
    arXiv:1711.02588
    GAMM-Mitteilungen, 40(4), p.339-350, 2018
    DOI: 10.1002/gamm.201740005
    Preprint SPP1962-031
  37. F. Harder and G. Wachsmuth
    Comparison of optimality systems for the optimal control of the obstacle problem
    GAMM-Mitteilungen, 40(4), p.312-338, 2018
    DOI: 10.1002/gamm.201740004
    Preprint SPP1962-029
  38. T. Etling and R. Herzog
    Optimum Experimental Design by Shape Optimization of Specimens in Linear Elasticity
    SIAM Journal on Applied Mathematics, 78(3), p.1553-1576, 2018
    DOI: 10.1137/17M1147743
  39. G. Wachsmuth
    A guided tour of polyhedric sets
    Journal of Convex Analysis, 26(1), p.153--188, 2019
  40. Goldberg, Niels, Ospald, Felix and Schneider, Matti
    A fiber orientation-adapted integration scheme for computing the hyperelastic Tucker average for short fiber reinforced composites
    Computational Mechanics (CM), 60(4), p.595-611, 2017
    DOI: 10.1007/s00466-017-1425-0
  41. B. González Merino, T. Jahn, A. Polyanskii and G. Wachsmuth
    Hunting for reduced polytopes
    arXiv:1701.08629
    Discrete & Computational Geometry , 60(3), p.801-808, 2018
    DOI: 10.1007/s00454-018-9982-3
    Code: Hunting for reduced polytopes: Evaluating your catches (DOI: 10.5281/zenodo.58491)
  42. M. Herrmann, R. Herzog, H. Kröner, S. Schmidt and J. Vidal Núñez
    Analysis and an Interior Point Approach for TV Image Reconstruction Problems on Smooth Surfaces
    SIAM Journal on Imaging Sciences, 11(2), p.889-922, 2018
    DOI: 10.1137/17M1128022
  43. P. Mehlitz and G. Wachsmuth
    The weak sequential closure of decomposable sets in Lebesgue spaces and its application to variational geometry
    Set-Valued and Variational Analysis (SVAA), 27(1), p.265-294, 2017
    DOI: 10.1007/s11228-017-0464-1
    Preprint SPP1962-016
  44. S.-J. Kimmerle, M. Gerdts and R. Herzog
    Optimal Control of an Elastic Crane-Trolley-Load System - A Case Study for Optimal Control of Coupled ODE-PDE Systems
    Mathematical and Computer Modelling of Dynamical Systems, 24(2), p.182-206, 2018
    DOI: 10.1080/13873954.2017.1405046
  45. E. Casas, D. Wachsmuth and G. Wachsmuth
    Sufficient Second-Order Conditions for Bang-Bang Control Problems
    SIAM Journal on Control and Optimization (SICON), 55(5), p.3066-3090, 2017
    DOI: 10.1137/16M1099674
  46. R. Herzog and K. Soodhalter
    A modified implementation of MINRES to monitor residual subvector norms for block systems
    SIAM Journal on Scientific Computing, 39(6), p.A2645-A2663, 2017
    DOI: 10.1137/16M1093021
    arXiv:1603.04475
    Matlab code: SUBMINRES. A modified implementation of MINRES to monitor residual subvector norms for block systems
  47. C. Schneider and G. Wachsmuth
    Regularization and discretization error estimates for optimal control of ODEs with group sparsity
    ESAIM: Control, Optimisation and Calculus of Variations (COCV), 24(2), p.811--834, 2018
    DOI: 10.1051/cocv/2017049
  48. G. Wachsmuth
    Conforming Approximation of Convex Functions with the Finite Element Method
    Numerische Mathematik, 137(3), p.741-772, 2017
    DOI: 10.1007/s00211-017-0884-8
  49. A. Rösch and G. Wachsmuth
    Mass lumping for the optimal control of elliptic partial differential equations
    SIAM Journal on Numerical Analysis (SINUM), 55(3), p.1412-1436, 2017
    DOI: 10.1137/16M1074473
  50. U. Stefanelli, D. Wachsmuth and G. Wachsmuth
    Optimal control of a rate-independent evolution equation via viscous regularization
    Discrete and Continuous Dynamical Systems - Series S (DCDS-S), 10(6), p.1467-1485, 2017
    DOI: 10.3934/dcdss.2017076
    Preprint SPP1962-001
  51. P. Mehlitz and G. Wachsmuth
    The limiting normal cone to pointwise defined sets in Lebesgue spaces
    Set-Valued and Variational Analysis (SVAA), 26(3), p.449-467, 2018
    DOI: 10.1007/s11228-016-0393-4
    Preprint SPP1962-004
  52. R. Herzog and W. Wollner
    A Conjugate Direction Method for Linear Systems in Banach Spaces
    Journal of Inverse and Ill-Posed Problems, 25(5), p.553-572, 2017
    DOI: 10.1515/jiip-2016-0027
  53. R. Herzog, C. Meyer and A. Stötzner
    Existence of Solutions of a Thermoviscoplastic Model and Associated Optimal Control Problems
    Nonlinear Analysis: Real World Applications, 35, p.75-101, 2017
  54. Herzog, Roland and Ospald, Felix
    Parameter Identification for Short Fiber-Reinforced Plastics using Optimal Experimental Design
    International Journal for Numerical Methods in Engineering (NME), 110(8), p.703-725, 2017
    DOI: 10.1002/nme.5371
  55. G. Wachsmuth
    Pointwise Constraints in Vector-Valued Sobolev Spaces. With Applications in Optimal Control
    Applied Mathematics & Optimization (AMO), 77(3), p.463-497, 2016
    DOI: 10.1007/s00245-016-9381-1
  56. J.C. de los Reyes, R. Herzog and C. Meyer
    Optimal Control of Static Elastoplasticity in Primal Formulation
    Preprint SPP1253-151, 2013
    SIAM Journal on Control and Optimization, 54(6), p.3016-3039, 2016
    DOI: 10.1137/130920861
  57. Schneider, Matti, Ospald, Felix and Kabel, Matthias
    A model order reduction method for computational homogenization at finite strains on regular grids using hyperelastic laminates to approximate interfaces
    Computer Methods in Applied Mechanics and Engineering (CMAME), 309, p.476-496, 2016
    DOI: 10.1016/j.cma.2016.06.021
  58. G. Wachsmuth
    Strong stationarity for optimization problems with complementarity constraints in absence of polyhedricity
    Set-Valued and Variational Analysis (SVAA), 25(1), p.133-175, 2017
    DOI: 10.1007/s11228-016-0370-y
  59. J. Merger, A. Borzi and R. Herzog
    Optimal Control of a System of Reaction-Diffusion Equations Modeling the Wine Fermentation Process
    Optimal Control Applications and Methods, 38(1), p.112-132, 2017
    DOI: 10.1002/oca.2246
  60. G. Wachsmuth
    Towards M-stationarity for optimal control of the obstacle problem with control constraints
    SIAM Journal on Control and Optimization (SICON), 54(2), p.964-986, 2016
    DOI: 10.1137/140980582
  61. R. Schneider and G. Wachsmuth
    A-posteriori error estimation for control-constrained, linear-quadratic optimal control problems
    SIAM Journal on Numerical Analysis (SINUM), 54(2), p.1169-1192, 2016
    DOI: 10.1137/15M1020460
  62. R. Herzog and S. Mach
    Preconditioned Solution of State Gradient Constrained Elliptic Optimal Control Problems
    SIAM Journal on Numerical Analysis (SINUM), 54(2), p.688-718, 2016
    DOI: 10.1137/130948045
  63. A. Günnel and R. Herzog
    Optimal Control Problems in Finite-Strain Elasticity by Inner Pressure and Fiber Tension
    Frontiers in Applied Mathematics and Statistics, 2(4), 2016
    DOI: 10.3389/fams.2016.00004
  64. Schneider, Matti, Ospald, Felix and Kabel, Matthias
    Computational homogenization of elasticity on a staggered grid
    International Journal for Numerical Methods in Engineering (NME), 105(9), p.693-720, 2016
    DOI: 10.1002/nme.5008
  65. P. Mehlitz and G. Wachsmuth
    Weak and strong stationarity in generalized bilevel programming and bilevel optimal control
    Optimization, 65(5), p.907-935, 2016
    DOI: 10.1080/02331934.2015.1122007
  66. E. Casas, R. Herzog and G. Wachsmuth
    Analysis of Spatio-Temporally Sparse Optimal Control Problems of Semilinear Parabolic Equations
    ESAIM: Control, Optimisation and Calculus of Variations (COCV), 23(1), p.263-295, 2017
    DOI: 10.1051/cocv/2015048
  67. G. Wachsmuth
    Optimal Control of Quasistatic Plasticity with Linear Kinematic Hardening II: Regularization and Differentiability
    Zeitschrift für Analysis und ihre Anwendungen (ZAA), 34(4), p.391-418, 2015
    DOI: 10.4171/ZAA/1546
  68. G. Wachsmuth
    Optimal Control of Quasistatic Plasticity with Linear Kinematic Hardening III: Optimality Conditions
    Zeitschrift für Analysis und ihre Anwendungen (ZAA), 35(1), p.81-118, 2016
    DOI: 10.4171/ZAA/1556
  69. R. Herzog and E. Sachs
    Superlinear Convergence of Krylov Subspace Methods for Self-Adjoint Problems in Hilbert Space
    SIAM Journal on Numerical Analysis (SINUM), 53(3), p.1304-1324, 2015
    DOI: 10.1137/140973050
  70. G. Wachsmuth
    Mathematical programs with complementarity constraints in Banach spaces
    Journal of Optimization Theory and Applications (JOTA), 166(2), p.480-507, 2015
    DOI: 10.1007/s10957-014-0695-3
  71. R. Herzog, J. Obermeier and G. Wachsmuth
    Annular and Sectorial Sparsity in Optimal Control of Elliptic Equations
    Computational Optimization and Applications (COAP), 62(1), p.157-180, 2015
    DOI: 10.1007/s10589-014-9721-5
  72. R. Herzog and I. Riedel
    Sequentially optimal sensor placement in thermoelastic models for real time applications
    Optimization and Engineering, 16(4), p.737-766, 2015
    DOI: 10.1007/s11081-015-9275-0
  73. G. Wachsmuth
    Strong stationarity for optimal control of the obstacle problem with control constraints
    SIAM Journal on Optimization (SIOPT), 24(4), p.1914-1932, 2014
    DOI: 10.1137/130925827
  74. D. Wachsmuth and G. Wachsmuth
    Optimal Control of an Oblique Derivative Problem
    Mathematics and its Applications / Annals of AOSR, 6(1), 50-73, 2014
  75. G. Wachsmuth
    Differentiability of Implicit Functions: Beyond the Implicit Function Theorem
    Journal of Mathematical Analysis and Applications (JMAA), 414(1), p.259-272, 2014
    DOI: 10.1016/j.jmaa.2014.01.007
  76. A. Günnel, R. Herzog and E. Sachs
    A Note on Preconditioners and Scalar Products in Krylov Subspace Methods for Self-Adjoint Problems in Hilbert Space
    Electronic Transactions on Numerical Analysis, 41, p.13-20, 2014
  77. G. Wachsmuth
    The Numerical Solution of Newton's Problem of Least Resistance
    Mathematical Programming, 147(1-2), p. 331-350, 2014
    DOI: 10.1007/s10107-014-0756-2
  78. G. Wachsmuth, M. Lätzer and E. Leidich
    Analytical Computation of Multiple Interference Fits under Elasto-Plastic Deformations
    Journal of Applied Mathematics and Mechanics (ZAMM), 94, p.1058-1064, 2014
    DOI: 10.1002/zamm.201300041
  79. G. Wachsmuth
    On LICQ and the uniqueness of Lagrange multipliers
    Operations Research Letters (ORL), 41(1), p.78-80, 2013
    DOI: 10.1016/j.orl.2012.11.009
  80. R. Herzog, C. Meyer and G. Wachsmuth
    B- and Strong Stationarity for Optimal Control of Static Plasticity with Hardening
    Preprint SPP1253-114, 2011
    SIAM Journal on Optimization (SIOPT), 23(1), p.321-352, 2013
    DOI: 10.1137/110821147
  81. R. Herzog, K. Kunisch and J. Sass
    Primal-Dual Methods for the Computation of Trading Regions under Proportional Transaction Costs
    Mathematical Methods of Operations Research (MMOR), 77(1), p.101-130, 2013
    DOI: 10.1007/s00186-012-0416-3
  82. R. Herzog, C. Meyer and G. Wachsmuth
    C-Stationarity for Optimal Control of Static Plasticity with Linear Kinematic Hardening
    SIAM Journal on Control and Optimization (SICON), 50(5), p.3052-3082, 2012
    DOI: 10.1137/100809325
  83. G. Wachsmuth
    Optimal Control of Quasistatic Plasticity with Linear Kinematic Hardening, Part I: Existence and Discretization in Time (extended version)
    SIAM Journal on Control and Optimization (SICON), 50(5), p.2836-2861, 2012
    DOI: 10.1137/110839187
  84. E. Casas, R. Herzog and G. Wachsmuth
    Approximation of Sparse Controls in Semilinear Equations by Piecewise Linear Functions
    Numerische Mathematik, 122(4), p.645-669, 2012
    DOI: 10.1007/s00211-012-0475-7
  85. E. Casas, R. Herzog and G. Wachsmuth
    Optimality Conditions and Error Analysis of Semilinear Elliptic Control Problems with L1 Cost Functional
    SIAM Journal on Optimization (SIOPT), 22(3), p.795-820, 2012
    DOI: 10.1137/110834366
  86. D. Wachsmuth and G. Wachsmuth
    Regularization error estimates and discrepancy principle for optimal control problems with inequality constraints
    Control and Cybernetics, 40(4), p.1125-1158, 2011
  87. R. Herzog, G. Stadler and G. Wachsmuth
    Directional Sparsity in Optimal Control of Partial Differential Equations
    SIAM Journal on Control and Optimization (SICON), 50(2), p.943-963, 2012
    DOI: 10.1137/100815037
    Erratum: Directional Sparsity in Optimal Control of Partial Differential Equations
    DOI: 10.1137/15M102544X
  88. M. Bernauer and R. Herzog
    Implementation of an X-FEM Solver for the Classical Two-Phase Stefan Problem
    Journal of Scientific Computing, 52(2), p.271-293, 2012
    DOI: 10.1007/s10915-011-9543-x
  89. R. Herzog and F. Schmidt
    Weak Lower Semi-continuity of the Optimal Value Function and Applications to Worst-Case Robust Optimal Control Problems
    Optimization, 61(6), p.685-697, 2012
    DOI: 10.1080/02331934.2011.603322
  90. 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
  91. 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
  92. 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
  93. 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
  94. R. Herzog and K. Kunisch
    Algorithms for PDE-Constrained Optimization
    GAMM Reports, 33(2), p.163-176, 2010
    DOI: 10.1002/gamm.201010013
  95. 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)
  96. 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
  97. 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
  98. 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
  99. 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
  100. 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
  101. 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
  102. 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
  103. 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
  104. R. Griesse and D. Lorenz
    A Semismooth Newton Method for Tikhonov Functionals with Sparsity Constraints
    Inverse Problems, 24, 035007 (19pp), 2008
    elected one of the Highlights 2008 by the editorial board
    DOI: 10.1088/0266-5611/24/3/035007
    Matlab code: ssn.m
  105. J.C. de los Reyes and R. Griesse
    State-Constrained Optimal Control of the Three-Dimensional 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
  106. 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
  107. 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
  108. 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
  109. 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
  110. 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
  111. 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
  112. 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
  113. 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
  114. 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
  115. 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
  116. 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
  117. 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
  118. 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
  119. 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
  120. 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

Book Chapters

  1. O. Ferreira, M. Louzeiro and L. Prudente
    First Order Methods for Optimization on Riemannian Manifolds
    Springer, 2020
    DOI: 10.1007/978-3-030-31351-7_18
  2. R. Dietze, N. Goldberg, R. Herzog, S. Hannusch, M. Hofmann, J. Ihlemann, L. Kroll, A. Meyer, F. Ospald, E. Peretzki, G. Rünger, H. Schmidt, N. Schramm, R. Springer, M. Stockmann and L. Ulke-Winter
    Modellierung, integrative Simulation und Optimierung
    Springer, 2019
    DOI: 10.1007/978-3-662-54734-2_8
  3. J. Blechschmidt and R. Herzog
    Improving Policies for Hamilton-Jacobi-Bellman Equations by Postprocessing
    De Gruyter Radon Series on Computational and Applied Mathematics, 2018
    DOI: 10.1515/9783110543599-002
  4. C. Naumann, I. Riedel, U. Priber and R. Herzog
    Correction Algorithms and High-Dimensional Characteristic Diagrams
    in: Thermo-energetic Design of Machine Tools
    Lecture Notes in Production Engineering, p.159-174, Springer, 2015
  5. R. Herzog, C. Meyer and G. Wachsmuth
    Optimal Control of Elastoplastic Processes: Analysis, Algorithms, Numerical Analysis and Applications
    in: Trends in PDE Constrained Optimization
    International Series of Numerical Mathematics, p.27-41, Springer, 2014
  6. R. Herzog, A. Rösch, S. Ulbrich and W. Wollner
    OPTPDE: A Collection of Problems in PDE-Constrained Optimization
    in: Trends in PDE Constrained Optimization
    International Series of Numerical Mathematics, p.539-543, Springer, 2014

Publications in Proceedings

  1. R. Bergmann, M. Herrmann, R. Herzog, S. Schmidt and J. Vidal-Núñez
    Geometry Processing Problems Using the Total Variation of the Normal Vector Field
    Proceedings in Applied Mathematics and Mechanics (PAMM), 19(1), 2019
    DOI: 10.1002/pamm.201900189
  2. R. Bergmann, R. Herzog, E. Loayza and K. Welker
    Shape Optimization: what to do first, optimize or discretize?
    Proceedings in Applied Mathematics and Mechanics (PAMM), 19(1), 2019
    DOI: 10.1002/pamm.201900067
  3. P. Benner, R. Herzog, N. Lang, I. Riedel and J. Saak
    Optimal sensor placement based on model order reduction
    Proceedings of the CIRP sponsered Conference on Thermal Issues in Machine Tools, 2018
  4. Bergmann, Jean Pierre, Bielenin, Martin, Herzog, Roland, Hildebrand, Jörg, Riedel, Ilka, Schricker, Klaus, Trunk, Carsten and Worthmann, Karl
    Prevention of solidification cracking during pulsed laser beam welding
    Proceedings in Applied Mathematics and Mechanics (PAMM), 17(1), p.405-406, 2017
    DOI: 10.1002/pamm.201710172
  5. Ospald, Felix and Herzog, Roland
    Topology Optimization for Injection Molding of Short Fiber-Reinforced Plastics
    Proceedings in Applied Mathematics and Mechanics (PAMM), 17(1), p.337-338, 2017
    DOI: 10.1002/pamm.201710138
  6. R. Herzog and I. Riedel
    Optimale Sensorplatzierung und Online-Zustands- und Parameter-Identifikation
    Tagungsband des 5. Kolloquiums zum SFB/Transregio 96, 2017
  7. D. Wachsmuth and G. Wachsmuth
    How not to discretize the control
    arXiv:1603.07099
    Proceedings in Applied Mathematics and Mechanics (PAMM), 16(1), p.793-794, 2016
    DOI: 10.1002/pamm.201610385
  8. R. Herzog and K. Soodhalter
    Iterative Solution of Optimality Systems in Optimal Control
    in: Adaptive Methods for Control Problems Constrained by Time-Dependent PDEs
    Mathematisches Forschungsinstitut Oberwolfach, Report No. 04/2017, 2017
  9. Ospald, Felix and Herzog, Roland
    SIMP based Topology Optimization for Injection Molding of SFRPs
    Proceedings of the World Congress on Structural and Multidisciplinary Optimization (WCSMO), 2017
    DOI: 10.1007/978-3-319-67988-4_65
  10. Ospald, Felix and Herzog, Roland
    Optimal Experimental Design to Identify the Average Stress-Strain Response in Short Fiber-Reinforced Plastics
    Proceedings in Applied Mathematics and Mechanics (PAMM), 16(1), p.673-674, 2016
    DOI: 10.1002/pamm.201610325
  11. J. Glänzel, R. Herzog, S. Ihlenfeldt, A. Meyer and R. Unger
    Simulation-based correction approach for thermo-elastic workpiece deformations during milling process
    7th CIRP Conference on High Performance Cutting, 2016
    Procedia CIRP, 46, p.103-106, 2016
  12. R. Herzog, I. Riedel, B. Kauschinger and S. Schroeder
    Parameteridentifikation in thermo-elastischen Systemen
    Tagungsband des 4. Kolloquiums zum SFB/Transregio 96, 2016
  13. M. Kabel and A. Fink and F. Ospald and M. Schneider
    Nonlinear Composite Voxels and FFT-based Homogenization
    Proceedings of the ECCOMAS Congress, 2016
    DOI: 10.7712/100016.1944.5977
  14. C. Naumann, I. Riedel, S. Ihlenfeldt and U. Priber
    Characteristic diagram based correction algorithms for the thermo-elastic deformation of machine tools
    48th CIRP Conference on Manufacturing Systems, 2015
    Procedia CIRP, 41, p.801-805, 2016
  15. Schneider, Matti and Ospald, Felix and Kabel, Matthias
    Computational homogenization of elasticity at large deformations on a staggered grid
    Conference Proceedings of the YIC GACM, p.178-181, 2015
    URN: urn:nbn:de:hbz:82-rwth-2015-039806
  16. R. Schneider and G. Wachsmuth
    Achieving optimal convergence order for FEM in control constrained optimal control problems
    Proceedings in Applied Mathematics and Mechanics (PAMM), 15(1), p.731-734, 2015
    DOI: 10.1002/pamm.201510350
  17. S. Frankeser, S. Hiller, G. Wachsmuth and J. Lutz
    Using the On-state-Vbe Sat-Voltage for Temperature Estimation of SiC-BJTs During Normal Operation
    Proceedings of PCIM Europe 2015, p.132-139, 2015
  18. S. Hannusch, R. Herzog, M. Hofmann, J. Ihlemann, L. Kroll, A. Meyer, F. Ospald, G. Rünger, R. Springer, M. Stockmann and L. Ulke-Winter
    Efficient Simulation, Optimization, and Validation of Lightweight Structures
    Proceedings of the 2nd International MERGE Technologies Conference for Lightweight Structures (IMTC 2015), Chemnitz
    ISBN: 978-3-95735-025-1
  19. S. Takacs
    Using Cylindrical Algebraic Decomposition and Local Fourier Analysis to Study Numerical Methods: Two Examples
    Proceedings of 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, p.42-49, 2014
    DOI: 10.1109/SYNASC.2014.14
  20. Ospald, Felix
    Numerical Simulation of Injection Molding using OpenFOAM
    Proceedings in Applied Mathematics and Mechanics (PAMM), 14(1), p.673-674, 2014
    DOI: 10.1002/pamm.201410320
  21. R. Herzog and I. Riedel
    Comparison of Two Suboptimal Sensor Placement Strategies in Thermo-Elastic Models
    Special Issue: GAMM Annual Meeting 2014, Erlangen
    Proceedings in Applied Mathematics and Mechanics (PAMM), 14(1), p.881-882, 2014
    DOI: 10.1002/pamm.201410421
  22. A. Günnel and R. Herzog
    Optimal Control of Large Deformation Elasticity by Fiber Tension
    Special Issue: GAMM Annual Meeting 2014, Erlangen
    Proceedings in Applied Mathematics and Mechanics (PAMM), 14(1), p.879-880, 2014
    DOI: 10.1002/pamm.201410420
  23. R. Herzog and O. Rheinbach
    Scalability of a FETI-DP Method for Optimal Control Problems
    Special Issue: GAMM Annual Meeting 2014, Erlangen
    Proceedings in Applied Mathematics and Mechanics (PAMM), 14(1), p.837-838, 2014
    DOI: 10.1002/pamm.201410399
  24. M. Hofmann, F. Ospald, H. Schmidt and R. Springer
    Programming support for the flexible coupling of distributed software components for scientific simulations
    Proceedings of the 9th International Conference on Software Engineering and Applications (ICSOFT-EA), p.506-511, 2014
  25. R. Herzog and O. Rheinbach
    FETI-DP Methods for Optimal Control Problems
    in: Domain Decomposition Methods in Science and Engineering XXI
    (21st International Conference on Domain Decomposition Methods, DD21 2012, Rennes, France, June 25-29, 2012)
  26. D. Wachsmuth and G. Wachsmuth
    Necessary conditions for convergence rates of regularizations of optimal control problems
    in: System and Modeling
    (25th IFIP TC 7 Conference, CSMO 2011, Berlin, Germany, September 12-16, 2011, Revised Selected Papers)
  27. 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, 2012
  28. 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
  29. 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
  30. 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
  31. 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
  32. 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
  33. 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
    Proceedings in Applied Mathematics and Mechanics (PAMM), 5(1), p.47-50, 2005
  34. 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
  35. 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
  36. 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
  37. 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
  38. 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

Further Documents

  1. A. Stötzner
    Optimal Control of Thermoviscoplasticity
    Dissertation, TU Chemnitz, 2018
  2. G. Wachsmuth
    Optimization problems with complementarity constraints in infinite-dimensional spaces
    Habilitation thesis, TU Chemnitz, 2017
    URN: urn:nbn:de:bsz:ch1-qucosa-227446
  3. A. Günnel
    Numerical Aspects in Optimal Control of Elasticity Models with Large Deformations
    Dissertation, TU Chemnitz, 2014
  4. T. Etling
    Optimale Versuchsplanung für die Bestimmung von Parametern bei Wärmeübergangsexperimenten (in German)
    Diploma Thesis, TU Chemnitz, 2012
  5. R. Herzog, C. Meyer and G. Wachsmuth
    Optimale Steuerung in der Elastoplastizität
    GAMM-Rundbrief 02/2012, p.16-20, 2012
  6. Gerd Wachsmuth
    Optimal control of quasistatic plasticity - An MPCC in function space
    Dissertation, TU Chemnitz, 2011
  7. R. Herzog
    Algorithms and Preconditioning in PDE-Constrained Optimization
    Extended lecture notes pertaining to a talk at the summer school Analysis and Numerics of PDE Constrained Optimization, Lambrecht, Germany
    July 2010
  8. M. Bernauer
    Motion Planning for the Two-Phase Stefan Problem in Level Set Formulation
    Dissertation, TU Chemnitz, 2010
  9. R. Griesse
    Stability and Sensitivity Analysis in Optimal Control of Partial Differential Equations
    Cumulative Habilitation Thesis, Karl Franzens University Graz, Austria, 2008
  10. G. Wachsmuth
    Elliptische Optimalsteuerungsprobleme unter Sparsity-Constraints (in German)
    Diploma Thesis, TU Chemnitz, 2008
  11. R. Griesse
    The RICAM Information Leaflet (Information for Incoming Ph.D. Students, Postdocs, and Visiting Scientists), 2005
  12. 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
  13. R. Griesse
    Optimale und suboptimale Steuerung der Navier-Stokes-Gleichungen (in German)
    Diploma Thesis, TU Clausthal, 1999