Publikationen Arnd Rösch

Dissertation - Habilitation

  • Arnd Rösch. Identifikation nichtlinearer Wärmeübergangsgesetze mit Methoden der Optimalen Steuerung. Dissertation, Technische Universität Chemnitz, 1995.
  • Arnd Rösch. Analysis schneller und stabiler Verfahren zur optimalen Steuerung partieller Differentialgleichungen. Habilitation, Technische Universität Berlin, 2001.

Publikationen in Journalen

  1. B.T. Kien, A. Rösch, N.H. Son, N.V.Tuyen. FEM for Semilinear Elliptic Optimal Control with Nonlinear and Mixed Constraints. Journal of Optimization Theory and Applications 197(1): 130-173,2023.
  2. M. Holtmannspötter, A. Rösch. Existence of optimal controls in absence of a weakly continuos control-to-state operator. Pure and Applied Functional Analysis 7(5): 1717-1732,2022.
  3. E. Casas, M. Mateos, A. Rösch. Numerical approximation of control problems of non-monotone and non-coercive semilinear elliptic equations. Numerische Mathematik 149(2):305-340,2021.
  4. M. Holtmannspötter, A. Rösch. A priori error estimates for the approximation of a nonsmooth optimal control problem governed by a coupled semilinear PDE-ODE system. SIAM Journal Control and Optimization 59(5):3329-3358,2021.
  5. M.Holtmannspötter, A. Rösch, B.Vexler. A priori error estimates for the space-time finite element discretization of an optimal control problem governed by a coupled PDE-ODE system. Mathematical Control and Related Fields 11(3):601-624,2021.
  6. C. Clason, V.H. Nhu, A. Rösch. Optimal control of a non-smooth quasilinear elliptic equation. Mathematical Control and Related Fields 11(3):521-554,2021.
  7. C. Clason, V.H. Nhu, A. Rösch. No-gap second-order optimality conditions for a non-smooth quasilinear elliptic equation. ESAIM COCV 27: Paper 62, 35pp,2021.
  8. E. Casas, M.Mateos, A. Rösch. Analysis of control problems of nonmonotone semilinear equations. ESAIM COCV 26: Paper 80, 21pp,2020.
  9. E. Casas,  M. Mateos, A. Rösch. Error Estimates for Semilinear Parabolic Control Problems in the Absence of Tikhonov Term.  SIAM Journal Control and Optimization 57(2):2515-2550,2019.
  10. K. Kohls, C. Kreuzer, A. Rösch and K.G.Siebert. Convergence of Adaptive Finite Element Methods for Optimal Control Problems with Control Constraints. North-West European Journal of Mathematics 4:157-184,2018.
  11. T. Apel, M. Mateos, J. Pfefferer and A. Rösch. Error estimates for Dirichlet control problems in polygonal domains: Quasi-uniform meshes. Mathematical Control and Related Fields 8(1):217-245,2018.
  12. E. Casas, M. Mateos and A. Rösch. Improved approximation rates for a parabolic control problem with an objective promoting directional sparsity. Computational Optimization and Applications 70(1), 239-266, 2018.
  13. A. Rösch, K.G. Siebert and S. Steinig. Reliable a posteriori error estimation for state-constrained optimal control. Computational Optimization and Applications 68(1), 121-162, 2017.
  14. E. Casas, M. Mateos and A. Rösch. Finite element approximation of sparse parabolic control problems. Mathematical Control and Related Fields 7(3): 393-417, 2017.
  15. A. Rösch and G. Wachsmuth. Mass Lumping for the Optimal Control of Elliptic Partial Differential Equations. SIAM Journal on Numerical Analysis 55(3): 1412-1436, 2017.
  16. B.T. Kien, A. Rösch and D. Wachsmuth. Pontryagin's principle for optimal control problem governed by 3D-Navier-Stokes equations. Journal of Optimization Theory and Applications 173(1): 30-55, 2017.
  17. N.H. Son, B.T. Kien and A. Rösch. Second-order optimality conditions for boundary control problems with mixed pointwise constraints. SIAM Journal on Optimization 26(3): 1912-1943, 2016.
  18. T. Apel, M. Mateos, J. Pfefferer and A. Rösch. On the Regularity of the Solutions of Dirichlet Optimal Control Problems in Polygonal Domains. SIAM Journal Control and Optimization 53(6): 3620-3641, 2015.
  19. I. Neitzel, J. Pfefferer and A. Rösch. Finite Element Discretization of State-Constrained Elliptic Optimal Control Problems with Semilinear State Equation. SIAM Journal Control and Optimization 53(2): 874-904, 2015.
  20. U. Aßmann and A. Rösch. Regularization in Sobolev Spaces with Fractional Order. Numerical Functional Analysis and Optimization 36(3): 271-286, 2015.
  21. B.T. Kien, V.H. Nhu and A. Rösch. Second-Order Necessary Optimality Conditions for a Class of Optimal Control Problems Governed by Partial Differential Equations with Pure State Constraints. Journal of Optimization Theory and Applications 165(1): 30-61, 2015.
  22. T. Apel, J. Pfefferer and A. Rösch. Finite element error estimates on the boundary with application to optimal control. Mathematics of Computation 84(291): 33-70, 2015.
  23. B.T. Kien, V.H. Nhu and A. Rösch. Lower semicontinuity of the solution map to a parametric elliptic optimal control problem with mixed pointwise constraints. Optimization 64(5):1219-1238, 2015.
  24. K. Kohls, A. Rösch and K.G. Siebert. A Posteriori Error Analysis of Optimal Control Problems with Control Constraints. SIAM Journal Control and Optimization 52(3): 1832-1861, 2014.
  25. U. Aßmann and A. Rösch. Identification of an Unknown Parameter Function in the Main Part of an Elliptic Partial Differential Equation. Zeitschrift für Analysis und ihre Anwendungen, 32(2): 163–178, 2013.
  26. T. Apel, J. Pfefferer and A. Rösch. Finite element error estimates for Neumann boundary control problems on graded meshes. Computational Optimization and Applications, 52(1): 3-28, 2012.
  27. A. Rösch and D. Wachsmuth. A-posteriori error estimates for optimal control problems with state and control constraints. Numerische Mathematik, 120(4): 733-762, 2012.
  28. A. Rösch and S. Steinig. A priori error estimates for a state-constrained elliptic optimal control problem. ESAIM: Mathematical Modelling and Numerical Analysis, 46(5): 1107-1120, 2012.
  29. K. Krumbiegel, I. Neitzel and A. Rösch. Regularization for semilinear elliptic optimal control problems with pointwise state and control constraints. Computational Optimization and Applications, 52(1): 181-207, 2012.
  30. M. Mateos and A. Rösch. On saturation effects in the Neumann boundary control of elliptic optimal control problems. Computational Optimization and Applications, 49: 359-378, 2011.
  31. A. Rösch and D. Wachsmuth. Semi-smooth Newton Method for an optimal control problem with control and mixed control-state constraints. Optimization Methods and Software, 26(2):169--186, 2011.
  32. K. Krumbiegel, I. Neitzel and A. Rösch. Sufficient optimality conditions for the Moreau-Yosida-type regularization concept applied to semilinear elliptic optimal control problems with pointwise state constraints. Mathematics and its Applications / Annals of AOSR, 2(2): 222-246, 2010.
  33. K. Krumbiegel, C. Meyer and A. Rösch. A Priori Error Analysis for Linear Quadratic Elliptic Neumann Boundary Control Problems with Control and State Constraints. SIAM Journal Control and Optimization 48(8): 5108-5142, 2010.
  34. D. A. Lorenz and A. Rösch. Error estimates for joint Tikhonov- and Lavrentiev-regularization of constrained control problems. Applicable Analysis, 89(11): 1679–1691, 2010.
  35. R. Griesse, N. Metla, and A. Rösch. Local Quadratic Convergence of SQP for Elliptic Optimal Control Problems with Mixed Control-State Constraints. Control and Cybernetics, 39(3):717-738, 2010.
  36. W. Alt, R. Griesse, N. Metla, and A. Rösch. Lipschitz Stability for Elliptic Optimal Control Problems with Mixed Control-State Constraints. Optimization, 59(6): 833-849, 2010.
  37. T. Apel, A. Rösch and D. Sirch. L∞-Error Estimates on Graded Meshes with Application to Optimal Control. SIAM Journal Control and Optimization 48(3): 1771-1796, 2009.
  38. S. Cherednichenko and A. Rösch. Error Estimates for the Discretization of Elliptic Control Problems with Pointwise Control and State Constraints. Computational Optimization and Applications 44(1):27-55, 2009.
  39. K. Krumbiegel and A. Rösch. A virtual control concept for state constrained optimal control problems. Computational Optimization and Applications, 43(2):213-233, 2009.
  40. K. Krumbiegel and A. Rösch. On the regularization error of state constrained Neumann control problems. Control and Cybernetics 37(2): 369-392, 2008.
  41. A. Rösch and D. Wachsmuth. Numerical verification of optimality conditions. SIAM Journal Control and Optimization, 47(5):2557-2581,2008.
  42. S. Cherednichenko, K. Krumbiegel and A. Rösch. Error estimates for the Lavrentiev regularization of elliptic optimal control problems. Inverse Problems 24(5): 055003, 2008.
  43. S. Cherednichenko and A. Rösch. Error estimates for the regularization of optimal control problems with pointwise control and state constraints. Zeitschrift für Analysis und ihre Anwendungen, 27(2):195--212, 2008.
  44. R. Griesse, N. Metla, and A. Rösch. Convergence Analysis of the SQP method for Nonlinear Mixed-Constrained Elliptic Optimal Control Problems. ZAMM 88(10):776-792, 2008.
  45. K. Krumbiegel and A. Rösch. A new stopping criterion for iterative solvers for control constrained optimal control problems. Archives of Control Sciences, 18(1):17-42, 2008.
  46. W. Alt, N. Bräutigam, and A. Rösch. Error estimates for finite element approximations of elliptic control problems. Discussiones Mathematicae Differential Inclusions, Control and Optimization, 27: 7-22, 2007.
  47. T. Apel, A. Rösch, and G. Winkler. Optimal control in non-convex domains: a priori discretization error estimates. Calcolo, 44(3):137--158, 2007.
  48. A. Rösch and F. Tröltzsch. On regularity of solutions and Lagrange multipliers of optimal control problems for semilinear equations with mixed pointwise control-state constraints. SIAM Journal Control and Optimization, 46(3):1098--1115, 2007.
  49. A. Rösch and R. Simon. Superconvergence properties for optimal control problems discretized by piecewise linear and discontinuous functions. Numerical Functional Analysis and Optimization, 28(3):425--443, 2007.
  50. A. Rösch and D. Wachsmuth. Regularity of solutions for an optimal control problem with mixed control-state constraints. TOP, 14(2):263-278, 2006.
  51. A. Rösch and B. Vexler. Superconvergence in Finite Element Methods for the Optimal Control Problem of the Stokes Equations. SIAM Journal on Numerical Analysis, 44(5):1903--1920, 2006.
  52. A. Rösch and F. Tröltzsch. Existence of regular Lagrange multipliers for a nonlinear elliptic optimal control problem with pointwise control-state constraints. SIAM Journal Control and Optimization, 45(2): 548--564, 2006.
  53. C. Meyer, A. Rösch, and F. Tröltzsch. Optimal Control of PDEs with regularized pointwise state constraints. Computational Optimization and Applications, 33(2--3): 209--228, 2006.
  54. A. Rösch and F. Tröltzsch. Sufficient second-order optimality conditions for an elliptic optimal control problem with pointwise control-state constraints. SIAM Journal Optimization, 17(3):776--794, 2006.
  55. A. Rösch. Error estimates for linear-quadratic control problems with control constraints. Optimization Methods and Software, 21(1): 121--134, 2006.
  56. A. Rösch and R. Simon. Linear and discontinuous approximations for optimal control problems. Numerical Functional Analysis and Optimization, 26(3): 427--448, 2005.
  57. C. Meyer and A. Rösch. L∞-estimates for approximated optimal control problems. SIAM Journal Control and Optimization, 44(5): 1636--1649, 2005.
  58. A. Rösch and D. Wachsmuth. Regularity of the adjoint state of the instationary Navier-Stokes equations. Zeitschrift für Analysis und ihre Anwendungen, 24(1): 103--116, 2005.
  59. C. Meyer and A. Rösch. Superconvergence properties of optimal control problems. SIAM Journal Control and Optimization, 43(3): 970--985, 2004.
  60. A. Rösch. Error estimates for parabolic optimal control problems with control constraints. Zeitschrift für Analysis und ihre Anwendungen, 23(2): 353--376, 2004.
  61. A. Rösch and F. Tröltzsch. Sufficient second order optimality conditions for a parabolic optimal control problem with pointwise state constraints. SIAM Journal Control and Optimization, 42(1): 138--154, 2003.
  62. K. Kunisch and A. Rösch. Primal-Dual Active Set Strategy for a General Class of Constrained Optimal Control Problems. SIAM Journal Optimization, 13(2): 321--334, 2002.
  63. A. Rösch and F. Tröltzsch. Sufficient second order optimality condition for a state constrained optimal control problem of a weakly singular integral equation. Numerical Functional Analysis and Optimization, 23: 173--193, 2002.
  64. T. Grund and A. Rösch. Optimal control of a linear elliptic equation with a supremum-norm functional. Optimization Methods and Software, 15:299--329, 2001.
  65. A. Rösch. Stability estimates for the identification of nonlinear heat transfer laws. Inverse Problems, 12:743--756, 1996.
  66. A. Rösch. Frechet differentiability of the solution of the heat equation with respect to a nonlinear boundary condition. Zeitschrift für Analysis und ihre Anwendungen, 15(3):603--618, 1996.
  67. A. Rösch. Identification of nonlinear heat transfer laws by optimal control. Num. Funct. Analysis and Optimization, 15(3--4):417--434, 1994.
  68. A. Rösch and F. Tröltzsch. An optimal control problem arising from the identification of nonlinear heat transfer laws. Archives of Control Sciences, 1(3--4):183--195, 1992.

Veröffentlichungen in Tagungsbänden

  1. T. Apel, M. Mateos, J. Pfefferer, A. Rösch: Superconvergent graded meshes for an elliptic Dirichlet control problem. Advanced finite element methods and applications, Lecture Notes Compt. Sci. Eng. 128: pages 1-16, Springer, Cham 2019.
  2. R. Herzog, A. Rösch, S. Ulbrich, W. Wollner: OPTPDE: a collection of problems in PDE-constrained optimization. Trends in PDE constrained optimization, International series of Numerical Mathematics, Vol. 165: pages 539-543, Birkhäuser/Springer, Cham 2014.
  3. K. Kohls, a. Rösch, K.G. Siebert: Convergence of adaptive finite elements for optimal control problems with control constraints. Trends in PDE constrained optimization, International series of Numerical Mathematics, Vol. 165: pages 403-419, Birkhäuser/Springer, Cham 2014.
  4. T. Apel, J. Pfefferer, A. Rösch: Graded meshes in optimal control for elliptic partial differential equations: an overview. Trends in PDE constrained optimization, International series of Numerical Mathematics, Vol. 165: pages 285-302, Birkhäuser/Springer, Cham 2014.
  5. M. Hinze and A. Rösch. Discretization of optimal control problems. In Constrained Optimization and Optimal Control for Partial Differential Equations ed. G. Leugering, Sebastian Engell, Andreas Griewank, Michael Hinze, Rolf Rannacher, Volker Schulz, Michael Ulbrich, Stefan Ulbrich, International Series of Numerical Mathematics, Vol. 160: pages 391-431, Springer 2012.
  6. K. Kohls, A. Rösch, K.G. Siebert: A Posteriori Error Estimators for Control Constrained Optimal Control Problems. In Constrained Optimization and Optimal Control for Partial Differential Equations ed. G. Leugering, Sebastian Engell, Andreas Griewank, Michael Hinze, Rolf Rannacher, Volker Schulz, Michael Ulbrich, Stefan Ulbrich, International Series of Numerical Mathematics, Vol. 160: pages 431-443, Springer 2012.
  7. A. Rösch and D. Wachsmuth. How to check numerically the sufficient optimality conditions for infinite-dimensional optimization problems. In Optimal control of coupled systems of partial differential equations, ed. K. Kunisch, G. Leugering, J. Sprekels, F. Tröltzsch, pages 297-318, Birkhäuser 2009.
  8. M. Mateos and A. Rösch. On saturation effects in the Neumann boundary control of elliptic optimal control problems. Special Issue (ICIAM 07) of PAMM, 7(1): 1060505--1060506.
  9. A. Rösch. Finite Dimensional Approximation of Optimal Control Problems Governed by Partial Differential Equations. Proceedings of the 12th International Conference on Methods and Models in Automation and Robotics in Miedzyzdroje (Poland), 101--104, 2006.
  10. T. Apel, A. Rösch and G. Winkler. Discretization error estimates for an optimal control problem in a nonconvex domain. In Numerical Mathematics and Advanced Applications, Proceedings of ENUMATH 2005, the 6th European Conference on Numerical Mathematics and Advanced Applications, Santiago de Compostela, Spain, July 2005, pages 299-307, ed. A. Bermudez de Castro, D. Gomez, P. Quintela, and P. Salgado, Springer, Berlin, 2006.
  11. A. Rösch. A Gauss-Newton Method for the Identification of Nonlinear Heat Transfer Laws. In Optimal Control of Complex Structures. International conference in Oberwolfach, Germany, June 6-10, 2000, number 139 in ISNM, pages 217-230. Birkhäuser, 2002.
  12. A. Rösch. Second order optimality conditions and stability estimates for the identification of nonlinear heat transfer laws. In Control and estimation of distributed parameter systems. International conference in Vorau, Austria, July 14-20, 1996, number 126 in ISNM, pages 237-246. Birkhäuser, 1998.
  13. A. Rösch. Identification of nonlinear heat transfer laws by means of boundary data. In Progress in Industry (at ECMI 94), pages 405--412. Wiley--Teubner, 1996.