Preprints
Articles in Scientific Journals
- Axel Kröner, Carlos Rautenberg, and Sergio S. Rodrigues
Existence, uniqueness, and stabilization results for parabolic variational inequalities,
ESAIM: Control, Optimisation and Calculus of Variations, 29 (37), 2023.
- Michael Hintermüller and Axel Kröner
Differentiability properties for boundary control of fluid-structure interactions of linear elasticity with Navier-Stokes equations with mixed-boundary conditions in a channel,
Applied Mathematics and Optimization, 87(15), 2023, doi.
- Elisa Giesecke and Axel Kröner,
Classification with Runge-Kutta networks and feature space augmentation,
Journal of Computational Dynamics, 2021, 8(4): 495--520, doi.
- Axel Kröner and Heiko Kröner
A priori error estimates for finite element approximations of regularized level set flows in higher norms,
Applied Numerical Mathematics, 171, 2022, 307-328, doi.
- Axel Kröner and Heiko Kröner
Hyperplane separation type theorems in Hadamard manifolds,
Journal of Convex Analysis 29(2), 2022, 519--529.
- Wiebke Günther and Axel Kröner
A note on a bilevel problem for parameter learning for optimal control problems with the wave equation,
Port. Math. 78(3/4), 2021, pp. 367-390.
- M.Soledad Aronna, J.Frédéric Bonnans, Axel Kröner
State constrained control-affine parabolic problems II: Second order sufficient optimality conditions,
SIAM Journal on Control and Optimization 59 (2), 2021, 1628-1655, doi.
- M.Soledad Aronna, J.Frédéric Bonnans, Axel Kröner
State-constrained control-affine parabolic problems I: first and second order necessary optimality conditions,
Set-Valued and Variational Analysis, 29, 2021, 383-408 doi.
- M.Soledad Aronna, J.Frédéric Bonnans, Axel Kröner
Optimal control of PDEs in a complex space setting; application to the Schrödinger equation
SIAM Journal on Control and Optimization, 57(2), 1390–1412, 2019, doi.
- Axel Kröner, Athena Picarelli, and Hasnaa Zidani
Infinite horizon stochastic optimal control problems with running maximum cost
SIAM Journal on Control and Optimization 56(5), p. 3296–3319, 2018, HAL, doi
- J.Frédéric Bonnans, Axel Kröner
Variational analysis for options with stochastic volatility and multiple factors
SIAM Journal on Financial Mathematics, 9(2), 465–492., 2018,
HAL,
doi.
- M.Soledad Aronna, J.Frédéric Bonnans, Axel Kröner
Optimal control of infinite dimensional bilinear systems: Application to the heat and wave equation
Mathematical Programming 168(1), 717-757, 2018, doi.
M.Soledad Aronna, J.Frédéric Bonnans, Axel Kröner,
Correction to: Optimal control of infinite dimensional bilinear systems: application to the heat and wave equations,
Mathematical Programming, 170, 569–570, 2018 doi
- Axel Kröner, Eva Kröner, and Heiko Kröner
Finite element approximation of level set motion by powers of the mean curvature
SIAM Journal on Scientific Computing 40 (2018), no. 6, A4158–A4183, doi, HAL.
- Mickaël Chekroun, Axel Kröner, Honghu Liu
Galerkin approximations of nonlinear optimal control problems in Hilbert spaces
Electronic Journal of Differential Equations, 2017(189), 1-40, 2017.
- Jochen Garcke and Axel Kröner
Suboptimal feedback control of PDEs by solving HJB equations on adaptive sparse grids
Journal of Scientific Computing, Volume 70(1):1-28, 2017, doi.
- Dante Kalise, Axel Kröner, and Karl Kunisch
Local minimization algorithms for dynamic programming equations
SIAM Journal on Scientific Computing, 38(3), A1587–A1615, 2016.
doi
- Axel Kröner and Sergio S. Rodrigues
Remarks on the internal exponential stabilization to a nonstationary solution for 1D Burgers equations.
SIAM Journal on Control and Optimization, 53(2), 1020-1055, 2015.
doi
- Axel Kröner, Karl Kunisch, and Hasnaa Zidani
Optimal feedback control of undamped wave equations by solving a HJB equation.
ESAIM: Control, Optimisation and Calculus of Variations, 21(2):442-464, 2015.
doi
- Axel Kröner and Karl Kunisch
A minimum effort optimal control problem for the wave equation.
Computational Optimization and Applications, 57(1), 241-270, 2014.
doi
- Axel Kröner
Semi-smooth Newton methods for optimal control of the dynamical Lamé system with control constraints.
Numerical Functional Analysis and Optimization, Vol. 34(7), 741-769, 2013.
doi
- Axel Kröner
Adaptive finite element methods for optimal control of second order hyperbolic equations.
Computational Methods in Applied Mathematics, Vol. 11(2), 214 - 240, 2011.
doi
-
Axel Kröner, Karl Kunisch, and Boris Vexler
Semismooth Newton methods for optimal control of the wave equation with control constraints.
SIAM Journal on Control and Optimization, Vol. 49(2), 830 - 858, 2011.
doi
- Axel Kröner and Boris Vexler
A priori error estimates for elliptic optimal control problems with bilinear state equation.
Journal of Computational and Applied Mathematics, Vol. 230(2), 781 - 802, 2009.
doi
Scientific Articles in Proceedings
- Mickaël Chekroun, Axel Kröner, Honghu Liu
Galerkin approximations for the optimal control of nonlinear delay differential equations
In: Hamilton-Jacobi-Bellman Equations
Numerical Methods and Applications in Optimal Control
D. Kalise, K. Kunisch, Z. Rao (eds), Radon Series on Computational and Applied Mathematics 21, 2018.
- M.Soledad Aronna, J.Frédéric Bonnans, Axel Kröner
Optimal control of bilinear systems in a complex space setting
20th IFAC World Congress, IFAC-PapersOnLine, Vol. 50(1), 2872-2877, 2017.
- Axel Kröner and Sergio S. Rodrigues
Internal exponential stabilization to a nonstationary solution for 1D Burgers equations with piecewise constant controls.
Proceedings of the European Control Conference (ECC), 2015, pp. 2676-2681.
doi
- Maurizio Falcone, Dante Kalise, and Axel Kröner
A semi-Lagrangian scheme for Lp-penalized minimum time problems.
Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS) 2014, pp. 1798-1803.
- Dante Kalise and Axel Kröner
Reduced-order minimum time control of advection-reaction-diffusion systems via dynamic programming.
Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS) 2014, pp. 1196-1202.
- Axel Kröner
Adaptive Finite Element Methods for Optimal Control of Elastic Waves.
Proceedings of the 7th Vienna International Conference on Mathematical Modelling, Inge Troch and Felix Breitenecker (ed.), Vol. 7, 1112-1117, 2012.
doi
- Axel Kröner
Dual weighted residual method for
optimal control of hyperbolic equations of second order.
PAMM 11(1), 797 - 798, 2011.
doi
- Axel Kröner, Karl Kunisch, and Boris Vexler
Semismooth Newton methods for an optimal boundary control problem of wave equations.
Recent Advances in Optimization and its Applications in Engineering: Moritz Diehl, Francois Glineur, Elias Jarlebring, Wim Michiels (ed.),
Springer, 389-398, 2010.
doi
Theses
Technical Reports
Lecture notes
- Numerische Lineare Algebra, 2018
- Optimal control of partial differential equations, 2018
- Analysis I und II, 2024
- Gewöhnliche Differentialgleichungen, 2025
- Grundlagen der Optimierung, 2023
- Nichtglatte Optimierung, 2024
Reports in popular science