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Publications








2017
Set-oriented multiobjective optimal control of PDEs using proper orthogonal decomposition
To appear in KoMSO Post-Workshop Proceedings - Reduced-Order Modeling, 2017
with D. Beermann, M. Dellnitz and S. Peitz
Multiobjective PDE-constrained optimization using the reduced-basis method
Advances in Computational Mathematics, 43:945-972, 2017
with L. Iapichino and S. Ulbrich
POD-based economic optimal control of heat-convection phenomena
Submitted, 2017
with L. Mechelli
Reduced-Order Greedy Controllability of Finite Dimensional Linear Systems
Submitted, 2017
with G. Fabrini and L. Iapichino
POD-based error control for reduced-order bicriterial PDE-constrained optimization
Annual Reviews in Control, 44, 226-237, 2017
with S. Banholzer and D. Beermann
Error analysis for POD approximations of infinite horizon problems via the dynamic programming approach
SIAM Journal on Control and Optimization, 55:3091-3115, 2017
with A. Alla and M. Falcone
POD-based multiobjective optimal control of PDEs with non-smooth objectives
To appear in PAMM, 2017
With D. Beermann, M. Dellnitz and S. Peitz
POD-based mixed-integer optimal control of the heat equation
Submitted, 2017
with F. Bachmann, D. Beermann and J. Lu
Optimization of hybrid multi-carrier energy supply networks
Submitted, 2017
with J. Lu, D. Beermann and D. König
Personalized medicine: optimization of EPO dosing
Submitted, 2017
with D. Fürtinger, F. Kappel, P. Kotanko and S. Rogg
Trust-region POD using a-posteriori error estimation for semilinear parabolic optimal control problems
Technical Report, Konstanzer Schriften in Mathematik, No. 359, 2017
with S. Rogg and S. Trenz
Mathematical Modeling and global optimization of hybrid energy supply networks
Technical Report, Konstanzer Schriften in Mathematik, No. 358, 2017
with J. Lu and M. Bernreuther
POD basis updates for nonlinear PDE control
at - Automatisierungstechnik, 65: 298-307, 2017
with C. Gräßle, M. Gubisch, S. Metzdorf and S. Rogg
Proper orthogonal decomposition for linear-quadratic optimal control
In P. Benner, A. Cohen, M. Ohlberger, and K. Willcox (eds.), Model Reduction and Approximation: Theory and Algorithms. pages 5-66, SIAM, Philadelphia, PA, 2017
with M. Gubisch
A-posteriori error estimation of discrete POD models for PDE-constrained optimal controls
In P. Benner, M. Ohlberger, A.T. Patera, G. Rozza, and K. Urban (eds.), Model Reduction of Parametrized Systems, Springer-Series Modeling, Simulation and Applications, 17:213-234, 2017
with M. Gubisch and I. Neitzel

2016
Reduced-order multiobjective optimal control of semilinear parabolic problems
Numerical Mathematics and Advanced Applications (ENUMATH 2015), Lecture Notes in Computational Science and Engineering, 112:389-397, 2016
with L. Iapichino and S. Trenz
POD-based bicriterial optimal control by the reference point method
IFAC-PapersOnLine, 49:210-215, 2016
with S. Banholzer and D. Beermann
A-posteriori error analysis for lithium-ion concentrations in batteries utilizing the reduced basis method
Mathematical and Computer Modelling of Dynamical Systems, 22:362-379, 2016
with L. Iapichino and A. Wesche

2015
Proper Orthogonal Decomposition zur Optimalsteuerung linearer partieller Differentialgleichungen
In Elektrische Antriebe - Regelung von Antriebssystemen von Dirk Schröder, pp. 1658-1684, Springer-Verlag, 2015
Asymptotic stability of POD based model predictive control for a semilinear parabolic PDE
Advances in Computational Mathematics, 41:1073-1102, 2015
with A. Alla
Optimality conditions and POD a-posteriori error estimates for a semilinear parabolic optimal control
Technical Report, Konstanzer Schriften in Mathematik, No. 345, 2015
with O. Lass and S. Trenz
Numerical analysis of optimality-system POD for constrained optimal control
Lecture Notes in Computational Science and Engineering, 105:297-317, Springer-Verlag, 2015
with E. Grimm and M. Gubisch
Parameter identification for nonlinear elliptic-parabolic systems with application in lithium-ion battery modeling
Computational Optimization and Applications, 62:217-239, 2015
with O. Lass
Optimization strategy for parameter sampling in the reduced basis method
IFAC-PapersOnLine, 48:707-712, 2015
with L. Iapichino

2014
Reduced basis method for the Stokes equations in decomposable domains using greedy optimization
ECMI 2014 proceedings, p. 1-7, ECMI book subseries of Mathematics in Industry, Heidelberg: Springer, 2014
with L. Iapichino, A. Quarteroni and G. Rozza
Model order reduction for PDE constrained optimization
In G. Leugering, P. Benner, S. Engell, A. Griewank, H. Harbrecht, M. Hinze, R. Rannacher, and S. Ulbrich (Eds.), Trends in PDE Constrained Optimization, International Series of Numerical Mathematics, Vol. 165, pages 303-326, Birkhäuser, Basel, 2014.
with P. Benner and E. Sachs
Adaptive POD basis computation for parametrized nonlinear systems using optimal snapshot location
Computational Optimization and Applications, 58:645-677, 2014
with O. Lass
POD a-posteriori error analysis for optimal control problems with mixed control-state constraints
Computational Optimization and Applications, 58:619-644, 2014
with M. Gubisch
Greedy sampling using nonlinear optimization
Proceedings of the CECAM Workshop on Reduced Basis, POD and Reduced Order Methods for model and computational reduction: towards real-time computing and visualization? In Reduced Order Methods for Modeling and Computational Reduction, A. Quarteroni and R. Rozza (eds.), pp. 137-157, Springer-Verlag, 2014
with K. Urban and O. Zeeb

2013
Greedy sampling of distributed parameters in the reduced-basis method by numerical optimization
with L. Iapichino
A method of a-posteriori error estimation with application to proper orthogonal decomposition
ESAIM: Mathematical Modelling and Numerical Analysis, 47:555-581, 2013
with E. Kammann and F. Tröltzsch
An inverse scattering problem for the time-dependent Maxwell equations: nonlinear optimization and model-order reduction
Numerical Linear Algebra with Applications, 20:689-711, 2013
with R. Mancini
POD Galerkin schemes for nonlinear elliptic-parabolic systems
SIAM Journal on Scientific Computing, 35(3):A1271-A1298, 2013
with O. Lass
Numerical analysis of POD a-posteriori error estimation for optimal control
In Control and Optimization with PDE Constraints, Kunisch, K.;Bredies, K.; Clason, C.; von Winckel (eds), International Series of Numerical Mathematics, Vol. 164, Birkhäuser, Basel, pp. 137-158, 2013
with A. Studinger
The reduced basis method applied to transport equations of a lithium-ion battery
COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 32:1760-1772, 2013
with A. Wesche

2012
POD a-posteriori error based inexact SQP method for bilinear elliptic optimal control problems
ESAIM: Mathemematical Modelling and Numerical Analysis, 46:491-511, 2012
with M. Kahlbacher
Model reduction techniques with a-posteriori error analysis for linear-quadratic optimal control problems
Numerical Algebra, Control and Optimization, 2:465-485, 2012
with G. Vossen

2011
Optimality system POD and a-posteriori error analysis for linear-quadratic problems
Control and Cybernetics, 40:1109-1125, 2011
Space mapping techniques for the optimization of a thickness parameter in the p-Laplace equation
Optimization Methods and Software, 26:617-642, 2011
with O. Lass, C. Posch, and G. Scharrer
Comparison of the reduced-basis and POD a-posteriori estimators for an elliptic linear-quadratic optimal control problem
Mathematical and Computer Modelling of Dynamical Systems, Special Issue: Model order reduction of parameterized problems, 17:355-369, 2011
with T. Tonn and K. Urban

2010
A space mapping approach for the p-Laplace equation
In Recent Advances in Optimization and its Applications in Engineering, Part 6, 399-408, 2010
with O. Lass
POD Galerkin approximations in PDE-constrained optimization
GAMM-Mitteilungen, 33:194-208, 2010
with E.W. Sachs
Mathematical optimization of a plate volume under a p-Laplace PDE constraint by using standard software
The Int. J. of Multiphysics, 4:1-11, 2010
with G. Scharrer and T. Heubrandtner
Optimal control of parameter-dependent convection-diffusion problems around rigid bodies
SIAM J. Sci. Comput., 32:1237-1260, 2010
with T. Tonn and K. Urban
Optimal snapshot location for computing POD basis functions
ESAIM: Mathemematical Modelling and Numerical Analysis. 44:509-529, 2010
with K. Kunisch
Admittance identification from point-wise sound pressure measurements using reduced-order modelling
Journal of Optimization Theory and Applications, 147:169-193, 2010

2009
POD a-posteriori error estimates for linear-quadratic optimal control problems
Computational Optimization and Applications, 44:83-115, 2009
with F. Tröltzsch
Mesh-independence and preconditioning for solving control problems with mixed control-state constraints
ESAIM: Control, Optimisation and Calculus of Variations, 15:626-652, 2009
with M. Hintermüller and I. Kopacka
Estimation of regularization parameters in elliptic optimal control problems by POD model reduction
In System Modelling and Optimization, A. Korytowski, K. Malanowski, W. Mitkowski, and M. Szymkat (eds.), 23rd IFIP TC 7 Conference, Cracow, Poland, July 23-27, 2007, Springer-Verlag, Berlin, 307-318, 2009
with M. Kahlbacher
A globalized Newton method for the accurate solution of a dipole quantum control problem
SIAM J. Sci. Comput. Volume 31:4176-4203, 2009
with G. von Winckel and A. Borzi

2008
Impedance identification by POD model reduction techniques
at-Automatisierungstechnik, 8:437-446, 2008
with A. Hepberger
Receding horizon controller for the baroreceptor loop in a model for the cardiovascular system
Cardiovascular Engineering, 8:14-22, 2008
with M. Mutsaers, M. Bachar, J. Batzel, and F. Kappel
Cascadic non-linear conjugate gradient solution to finite-level quantum optimal control problems
Journal of Computational and Applied Mathematics, 216:170-197, 2008
with A. Borzi and J. Salomon
Proper orthogonal decomposition for optimality systems
ESAIM: Mathemematical Modelling and Numerical Analysis, 42:1-23, 2008
with K. Kunisch
A sequential quadratic programming method for volatility estimation in option pricing
Journal on Optimization Theory and Applications, 139:515-540, 2008
with A. Jüngel and B. Düring
Error estimates for abstract linear-quadratic optimal control problems using proper orthogonal decomposition
Computational Optimization and Applications, 39:319-345, 2008
with M. Hinze
Objective vehicle dynamics evaluation of heavy commercial vehicles by means of model based parameter identifcation
In FISITA 2008, World Automotive Congress, Munich, Germany, 2008
with K. Prenninger and W. Hirschberg
Estimation of diffusion coefficients in a scalar Ginzburg-Landau equation by using model reduction
Numerical Mathematics and Advanced Applications. Proceedings of ENUMATH 2007, the 7th European Conference on Numerical Mathematics and Advanced Applications, Graz, Austria, September 2007, Kunisch, K.; Of, G.; Steinbach, O. (Eds.), Springer-Verlag, Heidelberg, 727-734, 2008
with M. Kahlbacher

2007
Optimal control of the stationary quantum drift-diffusion model
Communications in Mathematical Sciences, 5:85-111, 2007
with A. Unterreiter
Entwurf eines Sollwertgenerators für Fahrdynamikregelsysteme
Proceedings zum 15. Steierisches Seminar für Regelungstechnik und Prozessautomatisierung, Schloss Retzhof, 2007
with S. Eitzinger, W. Hirschberg, and W. Rosinger
A novel approach in vehicle dynamics. Parameter estimation of the non-linear sideslip stiffness
VDI-Berichte 1990, Erprobung und Simulation in der Fahrzeugentwicklung, (ISBN 978-3-18-091990-4), 13. VDI-Fachtagung, Würzburg, VDI Verlag GmbH, Düsseldorf, 359-374, 2007
with W. Hirschberg and P. Prenninger
Galerkin proper orthogonal decomposition methods for parameter dependent elliptic systems
Discussiones Mathematicae: Differential Inclusions, Control and Optimization, 27:95-117, 2007
with M. Kahlbacher
Fast solution techniques in constrained optimal boundary control of the semilinear heat equation
International Series of Numerical Mathematics, 155:119-147, 2007
with F. Diwoky and M. Hintermüller
Primal-dual active set methods for optimal control problems with mixed control-state and bilateral control constraints
Technical Report IMA04-07, University of Graz, 2007
with M. Hintermüller
A semismooth Newton method for semilinear optimal control problems with control-state and integral-state constraints
Technical Report IMA03-07, University of Graz, 2007
with M. Hintermüller and H. Müller

2006
SQP methods for parameter identification problems arising in hyperthermia
Optimization Methods and Software, 21:869-887, 2006
with T. Gänzler and M. Weiser
Reduced order output feedback control design for PDE systems using proper orthogonal decomposition and nonlinear semidefinite programming
Linear Algebra and Its Applications, 415:542-575, 2006
with F. Leibfritz
Analysis and assessment of the sensitivity of trim parameters on SEA simulations for interior noise reduction
Proceedings of the 13th International Congress on Sound and Vibration (ICSV), Vienna, Austria, 2006
with S. Brandl, I. Hauer, H.-H. Priebsch, and T. Bartosch
An algorithm for Galerkin projections in both time and spatial coordinates
Proceedings of the Seventeenth International Symposium on Mathematical Theory of Networks and Systems (MTNS), Kyoto, Japan, July 24-28, 2006
with S. Weiland
Impedance identification out of pressure datas with a hybrid measurement-simulation methodology up to 1kHz
In Proceedings of International Conference on Noise and Vibration Engineering, Leuven, Belgium, 2006
with F. Diwoky, A. Hepberger, and H.-H. Priebsch
Model reduction by proper orthogonal decomposition for lambda-omega systems
In Proceedings of European Conference on Computational Fluid Dynamics (ECCOMAS CFD), P. Wesseling, E. Onate, and J. Periaux (eds.), Egmont aan Zee, 2006
with M. Müller
Model reduction by proper orthogonal decomposition for estimation of scalar parameters in elliptic PDEs
In Proceedings of European Conference on Computational Fluid Dynamics (ECCOMAS CFD), P. Wesseling, E. Onate, and J. Periaux (eds.), Egmont aan Zee, 2006
with M. Kahlbacher
Parametric sensitivity analysis for optimal boundary control of a 3D reaction-diffusion system
Large-Scale Nonlinear Optimization. Series Nonconvex Optimization and Its Applications, Di Pillo and M. Roma (eds), Springer-Verlag, Berlin, 83:127-149, 2006
with R. Griesse
Numerical feedback controller design for PDE systems using model reduction: techniques and case studies
In L. Biegler and O. Ghattas and M. Heinkenschloss and D. Keyes and B. van Bloemen Waanders (eds.), Real-Time PDE-Constrained Optimization, SIAM, 2006
with F. Leibfritz

2005
Proper orthogonal decomposition surrogate models for nonlinear dynamical systems: error estimates and suboptimal control
In Reduction of Large-Scale Systems, P. Benner, V. Mehrmann, D. C. Sorensen (eds.), Lecture Notes in Computational Science and Engineering, Vol. 45, 261-306, 2005
with M. Hinze
A primal-dual active set strategy for optimal boundary control of a nonlinear reaction-diffusion system
SIAM Journal on Control and Optimization, 44:467-494, 2005
with R. Griesse

2004
HJB-POD based feedback design for the optimal control of evolution problems
SIAM Journal on Applied Dynamical Systems, 3:701-722, 2004
with K. Kunisch and L. Xie
On-line identification of hemodynamic variables by dilution off ultra-pure dialysate during hemodialysis
Cardiovascular Engineering, 4:39-46, 2004
with J. Wimmer, F. Kappel, B. Haditsch, H. Holzer, and D. Schneditz
Dynamical system based optimal control of incompressible fluids
International Journal for Numerical Methods in Fluids, 46:345-359, 2004
with M. Hintermüller, K. Kunisch, and Y. Spasov
Nonlinear conjugate gradient methods for the optimal control of laser surface hardening
Optimization Methods and Software, 18:179-199, 2004
Condition number of the stiffness matrices arising in POD Galerkin schemes for dynamical systems
PAMM Proc. Appl. Math. Mech., 4, 39-42, 2004
Optimal control strategies for the surface hardening of steel
2nd International Conference on Thermal Process Modelling and Computer Simulation Nancy, France, March 31 - April 2, 2003, Journal de Physique IV (Proceedings), S. Denis, P. Archambault, J.-M. Bergheau, R. Fortunier (eds.), 120:325-335, 2004
with D. Hömberg and W. Wolf
A semi-smooth Newton method for optimal boundary control of a nonlinear reaction-diffusion system
Proceedings of the Sixteenth International Symposium on Mathematical Theory of Networks and Systems (MTNS), Leuven, Belgium, July 5-9, 2004
with R. Griesse
Interpretation of proper orthogonal decomposition as singular value decomposition and HJB-based feedback design
Proceedings of the Sixteenth International Symposium on Mathematical Theory of Networks and Systems (MTNS), Leuven, Belgium, July 5-9, 2004

2003
Lagrange-SQP techniques for the control constrained optimal boundary control problems for the Burgers equation
Computational Optimization and Applications, 26:253-284, 2003
Control of laser surface hardening by a reduced-order approach using proper orthogonal decomposition
Mathematical and Computer Modeling, 38:1003-1028, 2003
with D. Hömberg
Laser surface hardening using proper orthogonal decomposition for a three-dimensional example
PAMM Proc. Appl. Math. Mech., 3, 1-4, 2003
with D. Hömberg
Upwind techniques and mixed finite elements for the steady-state Burgers equation
SFB-Preprint No. 278, 2003
Some remarks on augmented Lagrange-Newton SQP methods
SFB-Preprint No. 256, 2003
Optimal control of laser surface hardening by utilizing a nonlinear primal-dual active set strategy
SFB-Preprint No. 277, 2003
A globalized SQP method for the optimal control of laser surface hardening
SFB-Preprint No. 272, 2003

2002
Analysis of instantaneous control for the Burgers equation.
Nonlinear Analysis - Theory and Methods and Applications, 50:1-26, 2002
with M. Hinze
Mesh-independence of Lagrange-SQP methods with Lipschitz-continuous Lagrange multiplier updates
Optimization Methods and Software, 17:77-111, 2002
Augmented Lagrange-SQP methods with Lipschitz-continuous Lagrange multiplier updates
SIAM Journal on Numerical Analysis, 40:233-253, 2002
with E. Sachs
Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics
SIAM Journal on Numerical Analysis, 40:492-515, 2002
with K. Kunisch
Affine invariant convergence analysis for inexact augmented Lagrangian-SQP mehods
SIAM Journal on Control and Optimization, 41:875-899, 2002
with M. Weiser
Crank-Nicolson Galerkin proper orthogonal decomposition approximations for a general equation in fluid dynamics
18th GAMM Seminar on Multigrid and related methods for optimization problems, Leipzig, 97-114, 2002
with K. Kunisch

2001
Optimal control of a phase-field model using proper orthogonal decomposition
Zeitschrift für Angewandte Mathematik und Mechanik, 81:83-97, 2001
Distributed control problems for the Burgers equation
Computational Optimization and Applications, 18:115-140, 2001
The SQP method for control constrained optimal control of the Burgers equation
ESAIM: Control, Optimisation and Calculus of Variations, 6:649-674, 2001
with F. Tröltzsch
Galerkin proper orthogonal decomposition methods for parabolic problems
Numerische Mathematik, 90:117-148, 2001
with K. Kunisch
Second-order conditions for boundary control problems of the Burgers equation
Control and Cybernetics, 30:249-278, 2001
Nonlinear boundary control for the heat equation utilizing proper orthogonal decomposition
In K.-H. Hoffmann, R. H. W. Hoppe, V. Schulz, editors, Fast Solution of Discretized Optimization Problems, International Series of Numerical Mathematics, 138:73-87, 2001
with F. Diwoky
Boundary control of the Burgers equation: optimality conditions and reduced-order approach
In K.-H. Hoffmann, I. Lasiecka, G. Leugering, J. Sprekels, and F. Tröltzsch, editors, Optimal Control of Complex Structures, International Series of Numerical Mathematics, 139:267-278, 2001
Optimal and suboptimal control of partial differential equations: augmented Lagrange-SQP methods and reduced-order modeling with proper orthogonal decomposition
Habilitation Thesis, Karl-Franzens Universität Graz, 2001

2000
Application of the augmented Lagrangian-SQP method to optimal control problems for the stationary Burgers equation
Computational Optimization and Applications, 16:57-81, 2000
Mesh-independence for an augmented Lagrangian-SQP method in Hilbert spaces
SIAM Journal on Control and Optimization, 38:767-785, 2000

1999
Control of Burgers' equation by a reduced order approach using proper orthogonal decomposition
Journal on Optimization Theory and Applications, 102:345-371, 1999
with K. Kunisch

1997
Augmented Lagrangian-SQP techniques and their approximations
In S. Cox and I. Lasiecka, editors, Optimization Methods in Partial Differential Equations, volume 209 of Contemporary Mathematics, pages 147-159, 1997
with K. Kunisch
Mesh-independence of an augmented Lagrangian-SQP method in Hilbert spaces and control problems for the Burgers equation
Ph.D. Thesis, Fachbereich mathematik, TU Berlin, 1997

1993
Numerische Behandlung von absorbierenden Randbedingungen für hyperbolische Systeme
Diploma Thesis, Fachbereich mathematik, TU Berlin, 1993