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Optimal Control

Holder of the Professorship Optimal Control

Prof. Dr. Daniel Wachsmuth

Holder of the Professorship
Professorship for Mathematics at Chair of Mathematics VII
Emil-Fischer-Straße 30
97074 Würzburg
Building: 30 (Mathematik West)
Room: 02.011

 

Portrait Daniel Wachsmuth

  • Since 2012: Professor in Würzburg
  • 2008-2012: Postdoc at RICAM, Linz, Österreich
  • 2002-2008: Research Assistant, TU Berlin

  • optimal control of partial differential equations
  • nonsmooth optimization problems
  • regularisation of problems with bang-bang control

Publications

  • 1.
    A proximal gradient method for control problems with nonsmooth and nonconvex control cost
    Natemeyer, C., Wachsmuth, D.
    http://arxiv.org/abs/2007.11426 (2020)
     
  • 2.
    Full stability for variational Nash equilibriums of parametric optimal control problems of PDEs
    Qui, N. T., Wachsmuth, D.
    http://arxiv.org/abs/2002.08635 (2020)
     
  • 3.
    Safeguarded augmented Lagrangian methods in Banach spaces
    Karl, V., Kanzow, C., Steck, D., Wachsmuth, D.
    (2019)
     

  • 1.
    Optimal control of ODEs with state suprema
    Geiger, T., Wachsmuth, D., Wachsmuth, G.
    Math. Control Relat. Fields 11, 555-578 (2021)
     
  • 2.
    First and second order conditions for optimal control problems with an L^0 term in the cost functional
    Casas, E., Wachsmuth, D.
    SIAM J. Control Optim. 58, 3486–3507 (2020)
     
  • 3.
    Subgradients of marginal functions in parametric control problems of partial differential equations
    Qui, N. T., Wachsmuth, D.
    SIAM J. Opt. 30, 1724-1755 (2020)
     
  • 4.
    A Lagrange multiplier method for semilinear elliptic state constrained optimal control problems
    Karl, V., Neitzel, I., Wachsmuth, D.
    Comp. Opt. Appl. 831-869 (2020)
     
  • 5.
    Full stability for a class of control problems of semilinear elliptic partial differential equations
    Qui, N. T., Wachsmuth, D.
    SIAM J. Control Optim. 57, 3021-3045 (2019)
     
  • 6.
    Iterative hard-thresholding applied to optimal control problems with L^0(Ω) control cost
    Wachsmuth, D.
    SIAM J. Control Optim. 57, 854-879 (2019)
     
  • 7.
    The multiplier-penalty method for generalized Nash equilibrium problems in Banach spaces
    Kanzow, C., Karl, V., Steck, D., Wachsmuth, D.
    SIAM J. Optim. 29, 767-793 (2019)
     
  • 8.
    An augmented Lagrange method for elliptic state constrained optimal control problems
    Karl, V., Wachsmuth, D.
    Comp. Opt. Appl. 69, 857-880 (2018)
     
  • 9.
    Second-order analysis and numerical approximation for bang-bang bilinear control problems
    Casas, E., Wachsmuth, D., Wachsmuth, G.
    SIAM J. Control Optim. 56, 4203-4227 (2018)
     
  • 10.
    Stability for bang-bang control problems of partial differential equations
    Qui, N. T., Wachsmuth, D.
    Optimization 67, 2157-2177 (2018)
     
  • 11.
    An augmented Lagrangian method for optimization problems in Banach spaces
    Steck, D., Kanzow, C., Wachsmuth, D.
    SIAM J. Control Optim. 56, 272-291 (2018)
     
  • 12.
    Tikhonov regularization of optimal control problems governed by semi-linear partial differential equations
    Pörner, F., Wachsmuth, D.
    Mathematical Control & Related Fields 8, 315-335 (2017)
     
  • 13.
    Pontryagin’s principle for optimal control problem governed by 3d Navier-Stokes equations
    Kien, B., Rösch, A., Wachsmuth, D.
    J. Optim. Theory Appl. 173, 30-55 (2017)
     
  • 14.
    Optimal control of a rate-independent evolution equation via viscous regularization
    Stefanelli, U., Wachsmuth, D., Wachsmuth, G.
    Discrete and Continuous Dynamical Systems - Series S 10, 1467-1485 (2017)
     
  • 15.
    On the switching behavior of sparse optimal controls for the one-dimensional heat equation
    Tröltzsch, F., Wachsmuth, D.
    Mathematical Control & Related Fields 8, 135-153 (2017)
     
  • 16.
    Sufficient second-order conditions for bang-bang control problems
    Casas, E., Wachsmuth, D., Wachsmuth, G.
    SIAM J. Control Optim. 55, 3066-3090 (2017)
     
  • 17.
    Optimal control of interface problems with hp-finite elements
    Wachsmuth, D., Wurst, J.-E.
    Numerical Functional Analysis and Optimization 37, 363-390 (2016)
     
  • 18.
    An iterative Bregman regularization method for optimal control problems with inequality constraints
    Pörner, F., Wachsmuth, D.
    Optimization 65, 2195-2215 (2016)
     
  • 19.
    Functional error estimators for the adaptive discretization of inverse problems
    Clason, C., Kaltenbacher, B., Wachsmuth, D.
    Inverse Problems 32, 104004 (2016)
     
  • 20.
    The regularity of the positive part of functions in L^2(I;H^1(Ω)) ∩ H^1(I;H^1(Ω)^*) with applications to parabolic equations
    Wachsmuth, D.
    Comment. Math. Univ. Carolin. 57, 327-332 (2016)
     
  • 21.
    Exponential convergence of hp-finite element discretization of optimal boundary control problems with elliptic partial differential equations
    Wachsmuth, D., Wurst, J.-E.
    SIAM J. Control Optim. 54, 2526-2552 (2016)
     
  • 22.
    An interior point method designed for solving linear quadratic optimal control problems with $hp$ finite elements
    Wachsmuth, D., Wurst, J.-E.
    Optimization methods and software 30, 1276-1302 (2015)
     
  • 23.
    Newton methods for the optimal control of closed quantum spin systems
    Borzì, A., Ciaramella, G., Dirr, G., Wachsmuth, D.
    SIAM J. Sci. Comput. 37, A319-A346 (2015)
     
  • 24.
    Boundary concentrated finite elements for optimal control problems with distributed observation
    Beuchler, S., Hofer, K., Wachsmuth, D., Wurst, J.-E.
    Comp. Opt. Appl. 62, 31-65 (2015)
     
  • 25.
    Robust error estimates for regularization and discretization of bang-bang control problems
    Wachsmuth, D.
    Comp. Opt. Appl. 62, 271-289 (2014)
     
  • 26.
    Optimal control of an oblique derivative problem
    Wachsmuth, G., Wachsmuth, D.
    Ann. Acad. Rom. Sci. Ser. Math. Appl. 6, 50-73 (2014)
     
  • 27.
    On Time Optimal Control of the Wave Equation and its Numerical Realization as Parametric Optimization Problem
    Kunisch, K., Wachsmuth, D.
    SIAM J. Control Optim. 51, 1232-1262 (2013)
     
  • 28.
    On time optimal control of the wave equation, its regularization and optimality system
    Kunisch, K., Wachsmuth, D.
    ESAIM Control Optim. Calc. Var. 19, 317-336 (2013)
     
  • 29.
    Convergence analysis of smoothing methods for optimal control of stationary variational inequalities
    Schiela, A., Wachsmuth, D.
    ESAIM Math. Model. Numer. Anal. 47, 771-787 (2013)
     
  • 30.
    Adaptive regularization and discretization of bang-bang optimal control problems
    Wachsmuth, D.
    ETNA 40, 249-267 (2013)
     
  • 31.
    A-posteriori error estimates for optimal control problems with state and control constraints
    Rösch, A., Wachsmuth, D.
    Numerische Mathematik 120, 733-762 (2012)
     
  • 32.
    A-posteriori verification of optimality conditions for control problems with finite-dimensional control space
    Akindeinde, S., Wachsmuth, D.
    Numerical Functional Analysis and Optimization 33, 473-523 (2012)
     
  • 33.
    Boundary concentrated finite elements for optimal boundary control problems of elliptic PDEs
    Beuchler, S., Pechstein, C., Wachsmuth, D.
    Comp. Opt. Appl. 51, 883-908 (2012)
     
  • 34.
    Sufficient Optimality Conditions and Semi-Smooth Newton Methods for Optimal Control of Stationary Variational Inequalities
    Kunisch, K., Wachsmuth, D.
    ESAIM Control Optim. Calc. Var. 18, 520-547 (2012)
     
  • 35.
    Semi-smooth Newton’s Method for an optimal control problem with control and mixed control-state constraints
    Rösch, A., Wachsmuth, D.
    Optimization methods and software 26, 169-186 (2011)
     
  • 36.
    Path-following for Optimal Control of Stationary Variational Inequalities
    Kunisch, K., Wachsmuth, D.
    Comp. Opt. Appl. 51, 1345-1373 (2011)
     
  • 37.
    Convergence and regularization results for optimal control problems with sparsity functional
    Wachsmuth, G., Wachsmuth, D.
    ESAIM Control Optim. Calc. Var. 17, 858-886 (2011)
     
  • 38.
    On the regularization of optimization problems with inequality constraints
    Wachsmuth, G., Wachsmuth, D.
    Control and Cybernetics 4, 1125-1154 (2011)
     
  • 39.
    Optimal control of planar flow of incompressible non-Newtonian fluids
    Roubívcek, T., Wachsmuth, D.
    J. for Analysis and its Applications 29, 351-376 (2010)
     
  • 40.
    Optimal Dirichlet boundary control of Navier-Stokes equations with state constraint
    John, C., Wachsmuth, D.
    Numerical Functional Analysis and Optimization 30, 1309-1338 (2009)
     
  • 41.
    Sensitivity analysis and the adjoint update strategy for optimal control problems with mixed control-state constraints
    Griesse, R., Wachsmuth, D.
    Comp. Opt. Appl 44, 57-81 (2009)
     
  • 42.
    Update strategies for perturbed nonsmooth equations
    Griesse, R., Grund, T., Wachsmuth, D.
    Optimization methods and software 23, 321-343 (2008)
     
  • 43.
    Numerical verification of optimality conditions
    Rösch, A., Wachsmuth, D.
    SIAM J. Control Optim. 47, 2557-2581 (2008)
     
  • 44.
    Analysis of the SQP-method for optimal control problems governed by the instationary Navier-Stokes equations based on $L^p$-theory
    Wachsmuth, D.
    SIAM J. Control Optim. 46, 1133-1153 (2007)
     
  • 45.
    Second-order sufficient optimality conditions for the optimal control of Navier-Stokes equations
    Tröltzsch, F., Wachsmuth, D.
    ESAIM: COCV 12, 93-119 (2006)
     
  • 46.
    Regularity of solutions for an optimal control problem with mixed control-state constraints
    Rösch, A., Wachsmuth, D.
    TOP 14, 263-278 (2006)
     
  • 47.
    Sufficient second-order optimality conditions for convex control constraints
    Wachsmuth, D.
    J. Math. Anal. App. 319, 228-247 (2006)
     
  • 48.
    Regularity and Stability of optimal controls of instationary Navier-Stokes equations
    Wachsmuth, D.
    Control and Cybernetics 34, 387-410 (2005)
     
  • 49.
    Regularity of the adjoint state for the instationary Navier-Stokes equations
    Rösch, A., Wachsmuth, D.
    J. for Analysis and its Applications 24, 103-116 (2005)
     
  • 50.
    On convergence of a receding horizon method for parabolic boundary control
    Tröltzsch, F., Wachsmuth, D.
    Optimization methods and software 19, 201-216 (2004)
     
  • 51.
    On instantaneous control for a nonlinear parabolic boundary control problem
    Wachsmuth, D.
    Numerical Functional Analysis and Optimization 25, 151-181 (2004)
     

  • 1.
    How not to discretize the control
    Wachsmuth, D., Wachsmuth, G.
    In: Proceedings in Applied Mathematics and Mechanics. pp. 793-795 (2016)
     
  • 2.
    Upper and lower bounds on the set of recoverable strains and on effective energies in cubic-to-monoclinic martensitic phase transformations
    Schlömerkemper, A., Chenchiah, I., Fechte-Heinen, R., Wachsmuth, D.
    In: MATEC Web of Conferences 33 (2015)
     
  • 3.
    Necessary conditions for convergence rates of regularizations of optimal control problems
    Wachsmuth, G., Wachsmuth, D.
    In: Hömberg, D. and Tröltzsch, F. (eds.) System Modelling and Optimization. pp. 145-154. Springer (2013)
     
  • 4.
    Adaptive methods for control problems with finite-dimensional control space
    Akindeinde, S., Wachsmuth, D.
    In: Hömberg, D. and Tröltzsch, F. (eds.) System Modelling and Optimization. pp. 59-69. Springer (2013)
     
  • 5.
    Optimal Boundary Control Problems Related to High-Lift Configurations
    John, C., Noack, B. R., Schlegel, M., Tröltzsch, F., Wachsmuth, D.
    In: King, R. (ed.) Active Flow Control II. pp. 405-419. Springer, Berlin, Heidelberg (2010)
     
  • 6.
    Numerical Study of the Optimization of Separation Control
    Carnarius, A., Günther, B., Thiele, F., Wachsmuth, D., Tröltzsch, F., Reyes, J. C.
    In: Proceedings of the 45th AIAA Aerospace Sciences Meeting and Exhibit (2007)
     
  • 7.
    Numerical solution of optimal control problems with convex control constraints
    Wachsmuth, D.
    In: Ceragioli, F., Dontchev, A., Furuta, H., and Pandolfi, L. (eds.) Systems, Control, Modeling and Optimization. pp. 319-327. Springer (2006)
     
  • 8.
    Second-order sufficient optimality conditions for the optimal control of instationary Navier-Stokes equations
    Tröltzsch, F., Wachsmuth, D.
    In: Proceedings in Applied Mathematics and Mechanics. pp. 628-629 (2004)
     
  • 9.
    Fast closed loop control of the Navier-Stokes system
    Hinze, M., Wachsmuth, D.
    In: Bock, H. G., Kostina, E., Phu, H. X., and Rannacher, R. (eds.) Modelling, Simulation and Optimization of Complex Processes. pp. 189-202. Springer (2004)