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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
Phone: +49 931 31-89071
Fax: +49 931 31-84675
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.
    Spatially sparse optimization problems in fractional order Sobolev spaces
    Lentz, A., Wachsmuth, D.
    https://arxiv.org/abs/2402.14417 (2024)
  • 1.
    The largest-K-norm for general measure spaces and a DC Reformulation for L^0-Constrained Problems in Function Spaces
    Dittrich, B., Wachsmuth, D.
    https://arxiv.org/abs/2403.19437 (2024)
  • 1.
    Capacitary measures in fractional order Sobolev spaces: Compactness and applications to minimization problems
    Lentz, A.
    https://arxiv.org/abs/2412.11876 (2024)
  • 1.
    Non-monotone proximal gradient methods in infinite-dimensional spaces with applications to non-smooth optimal control problems
    Kanzow, C., Wachsmuth, D.
    (2023)
  • 1.
    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)

  • 1.
    A topological derivative-based algorithm to solve optimal control problems with L^0(Ω) control cost
    Wachsmuth, D.
    J Nonsmooth Anal. Opt. 5, (2024)
  • 1.
    Optimal control problems with L^0(Ω) constraints: maximum principle and proximal gradient method
    Wachsmuth, D.
    Comp. Opt. Appl. 87, 811-833 (2024)
  • 1.
    Optimal regularized hypothesis testing in statistical inverse problems
    Kretschmann, R., Wachsmuth, D., Werner, F.
    Inverse problems 40, 015013 (2024)
  • 1.
    Control in the coefficients of an elliptic differential operator: topological derivatives and Pontryagin maximum principle
    Wachsmuth, D.
    Mathematical Control & Related Fields (2024)
  • 1.
    Sparse optimization problems in fractional order Sobolev spaces
    Antil, H., Wachsmuth, D.
    Inverse problems 39, 044001 (2023)
  • 1.
    A Note on Existence of Solutions to Control Problems of Semilinear Partial Differential Equations
    Casas, E., Wachsmuth, D.
    SIAM J. Control Optim. 61, 1095-1112 (2023)
  • 1.
    A simple proof of the Baillon-Haddad theorem on open subsets of Hilbert spaces
    Wachsmuth, D., Wachsmuth, G.
    J. Convex Anal. 30, 1319-1328 (2023)
  • 1.
    Strong stationarity for optimal control problems with non-smooth integral equation constraints: Application to continuous DNNs
    Antil, H., Betz, L., Wachsmuth, D.
    Appl. Math. Optim. 88, (2023)
  • 1.
    A penalty scheme to solve constrained non-convex optimization problems in BV(Ω)
    Natemeyer, C., Wachsmuth, D.
    Pure Appl. Funct. Anal. 7, 1857–1880 (2022)
  • 1.
    Second-order conditions for non-uniformly convex integrands: quadratic growth in L^1
    Wachsmuth, D., Wachsmuth, G.
    J Nonsmooth Anal. Opt. 3, (2022)
  • 1.
    Optimal control of ODEs with state suprema
    Geiger, T., Wachsmuth, D., Wachsmuth, G.
    Math. Control Relat. Fields 11, 555-578 (2021)
  • 1.
    A proximal gradient method for control problems with non-smooth and non-convex control cost
    Natemeyer, C., Wachsmuth, D.
    Comp. Opt. Appl. 80, 639–677 (2021)
  • 1.
    Subgradients of marginal functions in parametric control problems of partial differential equations
    Qui, N. T., Wachsmuth, D.
    SIAM J. Opt. 30, 1724-1755 (2020)
  • 1.
    A Lagrange multiplier method for semilinear elliptic state constrained optimal control problems
    Karl, V., Neitzel, I., Wachsmuth, D.
    Comp. Opt. Appl. 831-869 (2020)
  • 1.
    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)
  • 1.
    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)
  • 1.
    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)
  • 1.
    Iterative hard-thresholding applied to optimal control problems with L^0(Ω) control cost
    Wachsmuth, D.
    SIAM J. Control Optim. 57, 854-879 (2019)
  • 1.
    An augmented Lagrangian method for optimization problems in Banach spaces
    Steck, D., Kanzow, C., Wachsmuth, D.
    SIAM J. Control Optim. 56, 272-291 (2018)
  • 1.
    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)
  • 1.
    An augmented Lagrange method for elliptic state constrained optimal control problems
    Karl, V., Wachsmuth, D.
    Comp. Opt. Appl. 69, 857-880 (2018)
  • 1.
    Stability for bang-bang control problems of partial differential equations
    Qui, N. T., Wachsmuth, D.
    Optimization 67, 2157-2177 (2018)
  • 1.
    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)
  • 1.
    Sufficient second-order conditions for bang-bang control problems
    Casas, E., Wachsmuth, D., Wachsmuth, G.
    SIAM J. Control Optim. 55, 3066-3090 (2017)
  • 1.
    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)
  • 1.
    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)
  • 1.
    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)
  • 1.
    An iterative Bregman regularization method for optimal control problems with inequality constraints
    Pörner, F., Wachsmuth, D.
    Optimization 65, 2195-2215 (2016)
  • 1.
    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)
  • 1.
    Optimal control of interface problems with hp-finite elements
    Wachsmuth, D., Wurst, J.-E.
    Numerical Functional Analysis and Optimization 37, 363-390 (2016)
  • 1.
    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)
  • 1.
    Functional error estimators for the adaptive discretization of inverse problems
    Clason, C., Kaltenbacher, B., Wachsmuth, D.
    Inverse Problems 32, 104004 (2016)
  • 1.
    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)
  • 1.
    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)
  • 1.
    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)
  • 1.
    Optimal control of an oblique derivative problem
    Wachsmuth, G., Wachsmuth, D.
    Ann. Acad. Rom. Sci. Ser. Math. Appl. 6, 50-73 (2014)
  • 1.
    Robust error estimates for regularization and discretization of bang-bang control problems
    Wachsmuth, D.
    Comp. Opt. Appl. 62, 271-289 (2014)
  • 1.
    Adaptive regularization and discretization of bang-bang optimal control problems
    Wachsmuth, D.
    ETNA 40, 249-267 (2013)
  • 1.
    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)
  • 1.
    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)
  • 1.
    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)
  • 1.
    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)
  • 1.
    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)
  • 1.
    A-posteriori error estimates for optimal control problems with state and control constraints
    Rösch, A., Wachsmuth, D.
    Numerische Mathematik 120, 733-762 (2012)
  • 1.
    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)
  • 1.
    Convergence and regularization results for optimal control problems with sparsity functional
    Wachsmuth, G., Wachsmuth, D.
    ESAIM Control Optim. Calc. Var. 17, 858-886 (2011)
  • 1.
    Path-following for Optimal Control of Stationary Variational Inequalities
    Kunisch, K., Wachsmuth, D.
    Comp. Opt. Appl. 51, 1345-1373 (2011)
  • 1.
    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)
  • 1.
    On the regularization of optimization problems with inequality constraints
    Wachsmuth, G., Wachsmuth, D.
    Control and Cybernetics 4, 1125-1154 (2011)
  • 1.
    Optimal control of planar flow of incompressible non-Newtonian fluids
    Roubívcek, T., Wachsmuth, D.
    J. for Analysis and its Applications 29, 351-376 (2010)
  • 1.
    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)
  • 1.
    Optimal Dirichlet boundary control of Navier-Stokes equations with state constraint
    John, C., Wachsmuth, D.
    Numerical Functional Analysis and Optimization 30, 1309-1338 (2009)
  • 1.
    Numerical verification of optimality conditions
    Rösch, A., Wachsmuth, D.
    SIAM J. Control Optim. 47, 2557-2581 (2008)
  • 1.
    Update strategies for perturbed nonsmooth equations
    Griesse, R., Grund, T., Wachsmuth, D.
    Optimization methods and software 23, 321-343 (2008)
  • 1.
    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)
  • 1.
    Sufficient second-order optimality conditions for convex control constraints
    Wachsmuth, D.
    J. Math. Anal. App. 319, 228-247 (2006)
  • 1.
    Second-order sufficient optimality conditions for the optimal control of Navier-Stokes equations
    Tröltzsch, F., Wachsmuth, D.
    ESAIM: COCV 12, 93-119 (2006)
  • 1.
    Regularity of solutions for an optimal control problem with mixed control-state constraints
    Rösch, A., Wachsmuth, D.
    TOP 14, 263-278 (2006)
  • 1.
    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)
  • 1.
    Regularity and Stability of optimal controls of instationary Navier-Stokes equations
    Wachsmuth, D.
    Control and Cybernetics 34, 387-410 (2005)
  • 1.
    On instantaneous control for a nonlinear parabolic boundary control problem
    Wachsmuth, D.
    Numerical Functional Analysis and Optimization 25, 151-181 (2004)
  • 1.
    On convergence of a receding horizon method for parabolic boundary control
    Tröltzsch, F., Wachsmuth, D.
    Optimization methods and software 19, 201-216 (2004)

  • 1.
    A numerical solution approach for non-smooth optimal control problems based on the Pontryagin maximum principle
    Wachsmuth, D.
    In: Gallego, R. and Mateos, M. (eds.) Proceedings of the French-German-Spanish Conference on Optimization (2024)
  • 1.
    Safeguarded augmented Lagrangian methods in Banach spaces
    Karl, V., Kanzow, C., Steck, D., Wachsmuth, D.
    In: Hintermüller, M., Herzog, R., Kanzow, C., Ulbrich, M., and Ulbrich, S. (eds.) Non-Smooth and Complementarity-Based Distributed Parameter Systems. pp. 241-282. Birkhäuser (2022)
  • 1.
    How not to discretize the control
    Wachsmuth, D., Wachsmuth, G.
    In: Proceedings in Applied Mathematics and Mechanics. pp. 793-795 (2016)
  • 1.
    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)
  • 1.
    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)
  • 1.
    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)
  • 1.
    Polynomial integration on regions defined by a triangle and a conic
    Sevilla, D., Wachsmuth, D.
    In: Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation ISSAC 2010. pp. 163-170. ACM, New York (2010)
  • 1.
    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)
  • 1.
    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)
  • 1.
    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)
  • 1.
    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)
  • 1.
    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)