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Optimal Control

Publications

You can find the complete publication list of Prof. Dr. Daniel Wachsmuth and the members of his research group on their personal websites:

> Project-related publications


  • Sparse optimization problems in fractional order Sobolev spaces Antil, H., Wachsmuth, D. http://arxiv.org/abs/2204.11456.
  • A simple proof of the Baillon-Haddad theorem on open subsets of Hilbert spaces Wachsmuth, D., Wachsmuth, G. http://arxiv.org/abs/2204.00282.
  • A Note on Existence of Solutions to Control Problems of Semilinear Partial Differential Equations Casas, E., Wachsmuth, D. http://arxiv.org/abs/2203.12996.
  • Optimal control problems with L^0(Ω) constraints: maximum principle and proximal gradient method Wachsmuth, D. http://arxiv.org/abs/2201.05360.
  • A penalty scheme to solve constrained non-convex optimization problems in BV(Ω) Natemeyer, C., Wachsmuth, D. http://arxiv.org/abs/2110.01849.
  • Full stability for variational {N}ash equilibriums of parametric optimal control problems of PDEs Qui, N. T., Wachsmuth, D. http://arxiv.org/abs/2002.08635.
  • Optimal control of an evolution equation with non-smooth dissipation Geiger, T., Wachsmuth, D. http://arxiv.org/abs/1801.04077.

2022[ to top ]
  • Sparse optimization problems in fractional order Sobolev spaces Antil, H., Wachsmuth, D. http://arxiv.org/abs/2204.11456.
  • Safeguarded augmented {L}agrangian methods in {B}anach spaces Karl, V., Kanzow, C., Steck, D., Wachsmuth, D. In: Hinterm"uller, M., Herzog, R., Kanzow, C., Ulbrich, M., and Ulbrich, S. (eds.) Non-Smooth and Complementarity-Based Distributed Parameter Systems. pp. 241-282. Birkh"auser.
  • A Note on Existence of Solutions to Control Problems of Semilinear Partial Differential Equations Casas, E., Wachsmuth, D. http://arxiv.org/abs/2203.12996.
  • Optimal control problems with L^0(Ω) constraints: maximum principle and proximal gradient method Wachsmuth, D. http://arxiv.org/abs/2201.05360.
  • Second-order conditions for non-uniformly convex integrands: quadratic growth in L^1 Wachsmuth, D., Wachsmuth, G. J Nonsmooth Anal. Opt. 3, .
  • A simple proof of the Baillon-Haddad theorem on open subsets of Hilbert spaces Wachsmuth, D., Wachsmuth, G. http://arxiv.org/abs/2204.00282.
2021[ to top ]
  • A penalty scheme to solve constrained non-convex optimization problems in BV(Ω) Natemeyer, C., Wachsmuth, D. http://arxiv.org/abs/2110.01849.
  • 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.
  • Optimal control of ODEs with state suprema Geiger, T., Wachsmuth, D., Wachsmuth, G. Math. Control Relat. Fields 11, 555-578.
2020[ to top ]
  • A {L}agrange multiplier method for semilinear elliptic state constrained optimal control problems Karl, V., Neitzel, I., Wachsmuth, D. Comp. Opt. Appl. 831-869.
  • 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.
  • Subdifferentials of marginal functions of parametric bang–bang control problems Qui, N. T. Nonlinear Analysis 195, 111743.
  • Full stability for variational {N}ash equilibriums of parametric optimal control problems of PDEs Qui, N. T., Wachsmuth, D. http://arxiv.org/abs/2002.08635.
2019[ to top ]
  • 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.
  • Iterative hard-thresholding applied to optimal control problems with L^0(Ω) control cost Wachsmuth, D. SIAM J. Control Optim. 57, 854-879.
  • 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.
  • On the uniqueness of non-reducible multi-player control problems Karl, V., P"orner, F. Optimization Methods and Software .
2018[ to top ]
  • 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.
  • Stability for bang-bang control problems of partial differential equations Qui, N. T., Wachsmuth, D. Optimization 67, 2157-2177.
  • Inexact Iterative {B}regman Method for Optimal Control Problems {P{"o}rner}, F. Numerical Functional Analysis and Optimization 39, 491-516.
  • A priori stopping rule for an iterative Bregman method for optimal control problems P"orner, F. Optimization Methods and Software 33, 249-267.
  • Regularization Methods for Ill-Posed Optimal Control Problems P{"o}rner, F. http://nbn-resolving.org/urn:nbn:de:bvb:20-opus-163153.
  • An augmented {L}agrange method for elliptic state constrained optimal control problems Karl, V., Wachsmuth, D. Comp. Opt. Appl. 69, 857-880.
  • 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.
  • 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.
  • A joint {T}ikhonov regularization and augmented {L}agrange approach for ill-posed state constrained control problems with sparse controls Karl, V., P"{o}rner, F. Numer. Funct. Anal. Optim. 39, 1543-1573.
2017[ to top ]
  • Sufficient second-order conditions for bang-bang control problems Casas, E., Wachsmuth, D., Wachsmuth, G. {SIAM} J. Control Optim. 55, 3066-3090.
  • On the switching behavior of sparse optimal controls for the one-dimensional heat equation Tr"oltzsch, F., Wachsmuth, D. Mathematical Control & Related Fields 8, 135-153.
  • Pontryagin’s principle for optimal control problem governed by 3d Navier-Stokes equations Kien, B., R"osch, A., Wachsmuth, D. J. Optim. Theory Appl. 173, 30-55.
  • 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.
  • Tikhonov regularization of optimal control problems governed by semi-linear partial differential equations P"orner, F., Wachsmuth, D. Mathematical Control & Related Fields 8, 315-335.
2016[ to top ]
  • 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.
  • An iterative {B}regman regularization method for optimal control problems with inequality constraints P"orner, F., Wachsmuth, D. Optimization 65, 2195-2215.
  • How not to discretize the control Wachsmuth, D., Wachsmuth, G. In: Proceedings in Applied Mathematics and Mechanics. pp. 793-795.
  • A sharp regularization error estimate for bang-bang solutions for an iterative Bregman regularization method for optimal control problems P"orner, F. In: Proceedings in Applied Mathematics and Mechanics. pp. 787-788.
  • 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.
  • Functional error estimators for the adaptive discretization of inverse problems Clason, C., Kaltenbacher, B., Wachsmuth, D. Inverse Problems 32, 104004.
  • Optimal control of interface problems with hp-finite elements Wachsmuth, D., Wurst, J.-E. Numerical Functional Analysis and Optimization 37, 363-390.