Publications

• 1.

  Spatially sparse optimization problems in fractional order Sobolev spaces Lentz, A., Wachsmuth, D. https://arxiv.org/abs/2402.14417 (2024).
  • [ arxiv ]
• 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).
  • [ arxiv ]
• 1.

  Capacitary measures in fractional order Sobolev spaces: Compactness and applications to minimization problems Lentz, A. https://arxiv.org/abs/2412.11876 (2024).
  • [ arxiv ]
• 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).
  • [ arxiv ]
• 1.

  Optimal control of an evolution equation with non-smooth dissipation Geiger, T., Wachsmuth, D. http://arxiv.org/abs/1801.04077 (2018).
  • [ arxiv ]

• 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).
  • [ DOI ]
  • [ arxiv ]
• 1.

  Optimal regularized hypothesis testing in statistical inverse problems Kretschmann, R., Wachsmuth, D., Werner, F. Inverse problems 40, 015013 (2024).
  • [ DOI ]
  • [ arxiv ]
• 1.

  Control in the coefficients of an elliptic differential operator: topological derivatives and Pontryagin maximum principle Wachsmuth, D. Mathematical Control & Related Fields (2024).
  • [ DOI ]
  • [ arxiv ]
• 1.

  Optimal control problems with L^0(Ω) constraints: maximum principle and proximal gradient method Wachsmuth, D. Comp. Opt. Appl. 87, 811-833 (2024).
  • [ DOI ]
  • [ arxiv ]
• 1.

  Sparse optimization problems in fractional order {S}obolev spaces Antil, H., Wachsmuth, D. Inverse problems 39, 044001 (2023).
  • [ DOI ]
  • [ arxiv ]
• 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).
  • [ DOI ]
  • [ arxiv ]
• 1.

  A simple proof of the {B}aillon-{H}addad theorem on open subsets of {H}ilbert spaces Wachsmuth, D., Wachsmuth, G. J. Convex Anal. 30, 1319-1328 (2023).
  • [ arxiv ]
• 1.

  Second-order conditions for non-uniformly convex integrands: quadratic growth in L^1 Wachsmuth, D., Wachsmuth, G. J Nonsmooth Anal. Opt. 3, (2022).
  • [ DOI ]
  • [ arxiv ]
• 1.

  Optimal control of ODEs with state suprema Geiger, T., Wachsmuth, D., Wachsmuth, G. Math. Control Relat. Fields 11, 555-578 (2021).
  • [ DOI ]
  • [ arxiv ]
• 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).
  • [ DOI ]
  • [ arxiv ]
• 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).
  • [ DOI ]
  • [ arxiv ]
• 1.

  A {L}agrange multiplier method for semilinear elliptic state constrained optimal control problems Karl, V., Neitzel, I., Wachsmuth, D. Comp. Opt. Appl. 831-869 (2020).
  • [ DOI ]
  • [ arxiv ]
• 1.

  Subdifferentials of marginal functions of parametric bang–bang control problems Qui, N. T. Nonlinear Analysis 195, 111743 (2020).
  • [ DOI ]
• 1.

  On the uniqueness of non-reducible multi-player control problems Karl, V., Pörner, F. Optimization Methods and Software (2019).
  • [ DOI ]
  • [ arxiv ]
• 1.

  The multiplier-penalty method for generalized {N}ash equilibrium problems in {B}anach spaces Kanzow, C., Karl, V., Steck, D., Wachsmuth, D. SIAM J. Optim. 29, 767-793 (2019).
  • [ DOI ]
• 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).
  • [ DOI ]
  • [ arxiv ]
• 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).
  • [ DOI ]
  • [ arxiv ]
• 1.

  A joint {T}ikhonov regularization and augmented {L}agrange approach for ill-posed state constrained control problems with sparse controls Karl, V., P{ö}rner, F. Numer. Funct. Anal. Optim. 39, 1543-1573 (2018).
  • [ DOI ]
  • [ arxiv ]
• 1.

  Stability for bang-bang control problems of partial differential equations Qui, N. T., Wachsmuth, D. Optimization 67, 2157-2177 (2018).
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  • [ arxiv ]
• 1.

  Inexact Iterative {B}regman Method for Optimal Control Problems {P{ö}rner}, F. Numerical Functional Analysis and Optimization 39, 491-516 (2018).
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  • [ arxiv ]
• 1.

  An augmented {L}agrangian method for optimization problems in {B}anach spaces Steck, D., Kanzow, C., Wachsmuth, D. {SIAM} J. Control Optim. 56, 272-291 (2018).
  • [ DOI ]
  • [ arxiv ]
• 1.

  A priori stopping rule for an iterative Bregman method for optimal control problems Pörner, F. Optimization Methods and Software 33, 249-267 (2018).
  • [ DOI ]
  • [ arxiv ]
• 1.

  Error estimates for the approximation of a discrete-valued optimal control problem Clason, C., Do, T. B. T., Pörner, F. Comp. Opt. Appl. 71, 857-878 (2018).
  • [ DOI ]
  • [ arxiv ]
• 1.

  An augmented {L}agrange method for elliptic state constrained optimal control problems Karl, V., Wachsmuth, D. Comp. Opt. Appl. 69, 857-880 (2018).
  • [ DOI ]
• 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).
  • [ DOI ]
  • [ arxiv ]
• 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).
  • [ DOI ]
  • [ arxiv ]
• 1.

  Sufficient second-order conditions for bang-bang control problems Casas, E., Wachsmuth, D., Wachsmuth, G. {SIAM} J. Control Optim. 55, 3066-3090 (2017).
  • [ DOI ]
• 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).
  • [ DOI ]
  • [ arxiv ]
• 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).
  • [ DOI ]
• 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).
  • [ DOI ]
• 1.

  An iterative {B}regman regularization method for optimal control problems with inequality constraints Pörner, F., Wachsmuth, D. Optimization 65, 2195-2215 (2016).
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  • [ arxiv ]
• 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).
  • [ DOI ]
• 1.

  Optimal control of interface problems with hp-finite elements Wachsmuth, D., Wurst, J.-E. Numerical Functional Analysis and Optimization 37, 363-390 (2016).
  • [ DOI ]
• 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).
  • [ DOI ]
• 1.

  Functional error estimators for the adaptive discretization of inverse problems Clason, C., Kaltenbacher, B., Wachsmuth, D. Inverse Problems 32, 104004 (2016).
  • [ DOI ]
  • [ arxiv ]

• 1.

  Safeguarded augmented {L}agrangian methods in {B}anach 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).
  • [ DOI ]
• 1.

  How not to discretize the control Wachsmuth, D., Wachsmuth, G. In: Proceedings in Applied Mathematics and Mechanics. pp. 793-795 (2016).
  • [ DOI ]
• 1.

  A sharp regularization error estimate for bang-bang solutions for an iterative Bregman regularization method for optimal control problems Pörner, F. In: Proceedings in Applied Mathematics and Mechanics. pp. 787-788 (2016).
  • [ DOI ]
  • [ arxiv ]

• 1.

  Regularization Methods for Ill-Posed Optimal Control Problems P{ö}rner, F. http://nbn-resolving.org/urn:nbn:de:bvb:20-opus-163153 (2018).

• 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).
  • [ arxiv ]
• 1.

  Capacitary measures in fractional order Sobolev spaces: Compactness and applications to minimization problems Lentz, A. https://arxiv.org/abs/2412.11876 (2024).
  • [ arxiv ]
• 1.

  Non-monotone proximal gradient methods in infinite-dimensional spaces with applications to non-smooth optimal control problems Kanzow, C., Wachsmuth, D. (2023).