Papers
Publications
Books
F. Tröltzsch,
Optimal Control of Partial Differential Equations - Theory, Methods and Applications.
Graduate Studies in Mathematics, Vol. 112. American Mathematical Society,
Providence, Rhode Island, 2010
(Translation of the second German edition below by J. Sprekels).
F. Tröltzsch, Optimale Steuerung partieller Differentialgleichungen - Theorie, Verfahren und
Anwendungen,
Vieweg, Wiesbaden 2005. Zweite Auflage: Vieweg+Teubner, Wiesbaden 2009.
Hoffmann, K.H., Lasiecka, I., Leugering,
G., Sprekels, J. and F. Tröltzsch (Eds.),
Optimal Control of Complex Structures,
International Series of Numerical Mathematics,
Vol. 139, Birkhäuser-Verlag 2002.
Hoffmann, K.H., Leugering,
G. and F. Tröltzsch (Eds.), Optimal Control
of Partial Differential Equations,
International Series of Numerical Mathematics, Vol. 133, Birkhäuser 1999.
Jentsch, L. and F. Tröltzsch (Eds.), Problems and Methods in Mathematical
Physics.
Teubner-Texte zur Mathematik Vol. 134, B.G. Teubner,
Stuttgart, Leipzig 1994.
F. Tröltzsch: Optimality conditions for parabolic control problems and applications.
Teubner-Texte zur Mathematik, Vol. 62, B.G. Teubner, Leipzig 1984.
Papers
(with K. Altmann and S. Stingelin)
On some optimal control problems for electric circuits.
Submitted to Int. Journal of Circuit Theory (2010).
(with I. Neitzel)
Numerical analysis of state-constrained optimal control problems for PDEs.
DFG Priority Program 1253, Techn. Report, 2010, to appear.
(with M. Hinze)
Discrete concepts versus error analysis in pde constrained optimization.
GAMM-Mitt. 33, No. 2, 148--162, 2010.
(with P. Merino and I. Neitzel)
On linear-quadratic elliptic control problems of semi-infinite type.
Accepted 2010 by Applicable Analysis.
(with P. Merino and I. Neitzel)
Error Estimates for the Finite Element Discretization of
Semi-infinite Elliptic Optimal Control Problems.
Accepted 2010 by Discussiones Mathematicae.
(with V. Dhamo)
Some aspects of reachability for parabolic boundary control problems
with control constraints.
To appear in Computational Optimization and Appl., DOI: 10.1007/s10589-009-9310-1
(with C. John, B.R. Noack, M. Schlegel and D. Wachsmuth)
Optimal boundary control problems related to high-lift configurations..
In: King, R. (Ed.), Active Flow Control II, Notes on Numerical Fluid Mechanics
and Multidisciplinary Design Vol. 108 (2010), 405-419. DOI: 10.1007/978-3-642-11735-0_26.
On Finite Element Error Estimates for Optimal Control Problems with
Elliptic PDEs.
In: Lirkov, I., Margenov, S., and Wasniewski, J. (Ed.), ''Large Scale-Scientific
Computing''.
Lecture Notes in Computer Science, Vol. 5910, pp. 40--53. Springer, 2010.
(with E. Casas)
Recent advances in the analysis of pointwise state-constrained
elliptic optimal control problems.
ESAIM: COCV Vol. 16, No. 3, 2010, pp. 581 -- 600.
(with P. Merino and B. Vexler)
Error estimates for the finite element approximation of a semilinear
elliptic control problem with
state constraints and finite dimensional
control space.
ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 44(1), 167 - 188, 2010.
(with E. Casas)
First- and second-order optimality conditions for a class of optimal control problems
with
quasilinear elliptic equations.
SIAM J. Control and Optimization 48, No. 2 (2009), 688--718.
(with E. Casas)
Recent advances in the analysis of state-constrained
elliptic optimal control problems.
In: K. Kunisch, G. Leugering, J. Sprekels, F. Tröltzsch (Eds.),
Optimal Control of Coupled Systems of Partial Differential Equations,
ISNM 158, pp. 57--72, Birkhäuser 2009.
(with S. Volkwein)
POD a-posteriori error estimates for linear-quadratic optimal control problems.
Computational Optimization and Applications 44 (1), (2009), 83-115.
(with I. Yousept)
A regularization method for the numerical solution of elliptic boundary control problems
with pointwise state constraints.
Computational Optimization and Applications 42 (1),
(2009), 43--63.
(with I. Yousept)
Source representation strategy for optimal boundary control problems
with state constraints.
Journal for Analysis and its Applications (ZAA)
28 (2009), 189-203.
(with I. Neitzel)
On regularization methods for the numerical solution of parabolic
control problems
with pointwise state constraints.
ESAIM: COCV
15 (2) (2009), 426-453.
(with J.C. de los Reyes, P. Merino, J. Rehberg)
Optimality conditions for state-constrained PDE control problems
with time-dependent controls.
To appear in Control and Cybernetics.
(with E. Casas and J.C. de Los Reyes)
Sufficient second-order optimality conditions for semilinear control
problems with
pointwise state constraints.
SIAM J. on Optimization 19, No. 2 (2008), 616--643.
(with I. Neitzel)
On convergence of regularization methods for nonlinear parabolic optimal
control problems
with control and state constraints.
Control and Cybernetics 37 (4), 2008.
(with M. Hintermüller and I. Yousept)
Mesh-independence of semismooth Newton methods for Lavrentiev-regularized
state constrained nonlinear optimal control problems.
Numerische Mathematik 108 (4), 2008, 571-603.
(with U. Prüfert and M. Weiser)
The convergence of an interior point method for an elliptic control
problem with
mixed control-state constraints.
Computational Optimization and Applications 39, No. 2 (2008), 183-218.
(with A. Carnarius, B. Günther, F. Thiele, D. Wachsmuth, J.C. De los Reyes)
Numerical Study of the Optimization of Separation Control.
Proceedings of the 45th AIAA Aerospace Sciences Meeting and Exhibit,
Reno, 8-11 January 2007, AIAA 2007-58.
(with U. Prüfert)
An interior point method for a parabolic optimal control problem
with regularized
pointwise state constraints.
ZAMM 87 (2007), No. 8-9, 564--589.
(with J.C. des los Reyes)
Optimal control of the stationary Navier-Stokes equations with mixed control-state constraints.
SIAM J. Control Optimization
46 (2), 604-629 (2007).
(with J.C. des los Reyes)
Flow control with regularized state constraints.
In: R. King (Ed.), Active Flow control. Springer, Berlin
2007, pp. 353--366.
(with A. Rösch)
On regularity of solutions and Lagrange multipliers of
optimal control problems for
semilinear equations with mixed pointwise control-state
constraints.
SIAM J. Control Optimization 46, No. 3 (2007), 1098-1115.
(with C. Meyer and U. Prüfert)
On two numerical methods for state-constrained elliptic control problems.
Optimization Methods and Software 22 (2007), 871-899.
(with A. Rösch)
Sufficient second-order optimality conditions for an elliptic optimal control
problem
with pointwise control-state constraints.
SIAM J. on Optimization 17, No. 3 (2006), 776--794.
(with C. Meyer and A. Rösch)
Optimal control problems of PDEs with regularized
pointwise state constraints.
Computational Optimization and Applications 33 (2006), 209--228.
(with A. Rösch)
Existence of regular Lagrange multipliers for a nonlinear
elliptic optimal control problem
with pointwise control-state
constraints.
SIAM J. Control and Optimization 45 (2) 2006, 548--564.
(with C. Meyer)
On an elliptic optimal control problem with pointwise
mixed control-state constraints.
In A. Seeger (Ed.)
Recent Advances in Optimization.
Proceedings of the 12th
French-German-Spanish Conference on Optimization
held in
Avignon, September 20-24, 2004.
Lectures Notes in Economics and Mathematical Systems, Vol. 563,
Springer-Verlag Berlin Heidelberg, 2006, 187-- 204.
(with D. Wachsmuth)
Second-order sufficient optimality conditions for
the optimal control of Navier-Stokes equations.
ESAIM COCV 12 (2006), no. 1, 93--119.
(with C. Meyer and P. Philip)
Optimal control of a semilinear PDE with nonlocal radiation
interface conditions.
SIAM J. Control Optim., 45 (2006), 699-721.
(with V. Maksimov)
Dynamical state and control resconstruction for a phase field model.
Dynamics of Continuous, Discrete and Impulsive Systems,
Ser. A Math. Analysis,
13 (2006), No. 3-4, 419--444.
Regular Lagrange multipliers for control problems with mixed
pointwise control-state constraints.
SIAM J. on Optimization 15, No. 2 (2005), 616--634.
(with E. Casas and M. Mateos)
Error estimates for the numerical approximation of
boundary semilinear elliptic control problems.
Computational Optimization and Applications 31, No. 2 (2005), 193--220.
(with D. Wachsmuth)
On convergence of a receding horizon method for
parabolic boundary control.
Optimization Methods and Software 19, No. 2 (2004),
201--216.
(with D. Wachsmuth)
Second-order sufficient optimality conditions for the optimal control of instationary Navier-Stokes
equations.
Proceedings in Applied Mathematics and Mechanics 4, No. 1 (2004), 628--629.
(with T. Roubicek)
Lipschitz stability of optimal controls for
the steady-state Navier-Stokes equations.
Control and Cybernetics 32 (2003), No. 3, 683--705.
(with A. Rösch)
Sufficient second order optimality condititions for a parabolic optimal control problem
with pointwise control-state constraints,
SIAM J. Control and Optimization 42 (2003), 138--154.
(with E. Casas)
Error estimates for linear-quadratic elliptic control problems.
In V. Barbu, et al. (Eds): Analysis and Optimization of
Differential Systems, pp. 89--100.
Kluwer Academic Publishers, Boston 2003.
(with E. Casas)
Error estimates for the finite-element
approximation of a semilinear elliptic control problem,
Control and Cybernetics 31 (2002), 695--712.
(with A. Rösch)
Sufficient second order optimality condititions for a state-constrained
optimal control problem
of a weakly singular integral equation,
Num. Funct. Anal. Appl. 23 (2002), 173--193.
(with N. Arada and J.-P. Raymond)
On an Augmented Lagrangian SQP Method
for a Class of Optimal Control Problems
in Banach Spaces,
Computational Optimization and Applications 22 (2002),
369--398.
(with N. Arada and E. Casas)
Error estimates for a semilinear elliptic
control problem,
Computational Optimization and Applications 23 (2002), 201--229.
(with E. Casas)
Second order necessary and sufficient optimality conditions for
optimization problems
and applications to control theory,
SIAM J. Optimization, 13 (2002), 406--431.
(with H. D. Mittelmann)
Sufficient Optimality in a Parabolic Control Problem,
In: A.H. Siddiqi, and M. Kocvara (Eds):
Trends in Industrial and Applied Mathematics,
Kluwer, Dordrecht, The Netherlands, 2002,
305--316.
(with W. Römisch)
Applied nonlinear optimization.
in: DFG Research Center Mathematics for Key Technologies,
Berliner Mathematische Gesellschaft, 2002, 21-37.
(with A. Unger)
Fast solution of optimal control problems in the selective
cooling of steel,
ZAMM 81 (2001), 447--456.
(with S. Volkwein)
The SQP method for control constrained optimal
control of the Burgers equation,
ESAIM: Control, Optimisation and Calculus of Variations, 6 (2001), 649-674.
(with K. Eppler)
Optimal Control Problems for the Nonlinear Heat Equation,
In: Online Optimization of Large Scale Systems,
Grötschel, M., Krumke, S.O.
and Rambau, J., Eds.,
Springer-Verlag Berlin 2001, 173--184.
(with K. Eppler)
Fast Optimization Methods in the Selective Cooling of Steel,
In: Online Optimization of Large Scale Systems,
Grötschel, M., Krumke, S.O. and Rambau, J., Eds.,
Springer-Verlag Berlin 2001, 185--204.
Lipschitz stability of solutions of linear-quadratic parabolic
control problems
with respect to perturbations.
Dynamics of Continuous, Discrete and Impulsive Systems
7 (2000), pp. 289 --306.
(with E. Casas and A. Unger)
Second order sufficient optimality conditions
for some state-constrained control problems
of semilinear elliptic
equations,
SIAM J. Control and Optimization 38 (2000), 1369--1391.
(with J.-P. Raymond)
Second order sufficient optimality conditions for
nonlinear parabolic control problems
with state constraints,
Discrete and Continuous Dynamical Systems 6 (2000), 431-450.
(with K. Malanowski)
Lipschitz stability of solutions to parametric optimal control for
elliptic equations,
Control and Cybernetics 29 (2000), 237--256.
(with M. Heinkenschloss)
Analysis of an SQP method for the control of a phase
field equation,
Control Cybernetics 28 (1999) No. 2, 177-211.
(with M. Bergounioux)
Optimal Control of Semilinear Parabolic Equations
with State-Constraints of Bottleneck Type,
ESAIM: Control, Optimisation and Calculus of
Variations 4 (1999), 595-608.
(with E. Casas)
Second order necessary optimality conditions for some
state-constrained
control problems of semilinear elliptic equations.
Appl. Math. Optimization 39 (1999), 211-228.
(with M. Bergounioux)
A linear parabolic boundary control problem with mixed
control-state constraint.
In: S. Chen, X. Li, J. Yong (Eds.),
Control of Distributed Parameter and Stochastic Systems,
Proceed. IFIP WG 7.2 Int. Conf., Hangzhou, June 19--22, 1998,
pp. 13--20, Kluwer Acad. Publ. 1999.
(with K. Malanowski)
Lipschitz stability of solutions to parametric optimal control for
parabolic equations,
Journal of Analysis and its Applications (ZAA),
18 (1999) 2, 469--489.
On the Lagrange-Newton-SQP Method for the Optimal Control of
Semilinear Parabolic Equations,
SIAM J. Control and
Optimization 38 (1999), 294--312.
(with H. Goldberg)
On a Lagrange-Newton method for a nonlinear parabolic
boundary control problem.
Optimization Methods
and Software 8 (1998), 225-247.
(with H. Goldberg)
On a SQP--multigrid technique for
nonlinear parabolic boundary control problems.
In
Optimal Control: Theory, Algorithms, and Applications.
W. W. Hager and P. M. Pardalos, Eds.,
Kluwer Academic Publishers
B.V., 1998, pp. 154--177.
(with M. Bergounioux)
Optimal Control of Linear Bottleneck Problems.
ESAIM: Control, Optimisation and Calculus of
Variations 3 (1998), 235-250.
(with W. Alt and H. Sontag)
An SQP method for optimal control of
weakly singular Hammerstein integral equations.
Appl. Math. Optimization 33 (1996), 227-252.
(with H. Goldberg and H. Sprekels)
Numerical treatment of a shape
optimization problem in thermoelasticity.
DFG-Preprint series "Anwendungsbezogene Optimierung und Steuerung", Report
No. 520.
(with D. Tiba)
Error estimates for the discretization of state constrained convex
control problems.
Num. Funct. Anal. Optimization 17 (1996), 1005--1028.
(with R. Lezius)
Theoretical and numerical aspects of controlled cooling of steel
profiles.
In: H. Neunzert (Ed.), Progress in Industrial Mathematics at ECMI 94,
380-388,
and Teubner 1996.
(with M. Bergounioux)
Optimality Conditions and Generalized Bang-Bang-Principle
for a State-Constrained
Semilinear Parabolic Problem.
Num. Funct. Anal. Optimization 17 (1996), 517--536.
(with E. Casas and A. Unger)
Second order sufficient optimality
conditions for a nonlinear elliptic control problem.
J. for Analysis and its Applications (ZAA) 15 (1996), 687 - 707.
A stability theorem for linear-quadratic parabolic
control problems.
In: Casas, E. (Ed.),
Control of partial differential equations and applications,
Lecture Notes
in Pure and Appl. Math. Vol. 174, pp. 287-296 (1996).
(with J. Sprekels)
On an optimal shape design problem connected with the heating of
elastic bodies.
Semidiscrete Ritz - Galerkin approximation of nonlinear parabolic
boundary control problems
- strong convergence of optimal controls.
Appl. Math. Optimization 29 (1994), 309 - 329.
An SQP method for optimal control of a nonlinear heat equation.
Control and Cybernetics 23 (1994), 267-288.
(with H. Goldberg)
Second order sufficient optimality conditions for a class of non-linear
parabolic
boundary control problems.
SIAM J. Contr. Opt. 31 (1993), 1007-1025.
(with A. Rösch)
An optimal control problem arising from the
identification of nonlinear heat transfer laws.
Archives of Control Sciences 1 (XXXVII) (1992), 183 - 195.
(with M. Hanke and J. Epperlein)
On a system of partial differential equations in photochemistry.
Wiss. Z. TU Chemnitz 34 (1992), 53-66.
(with H. Goldberg and W. Kampowsky)
On Nemytskii operators in Lp-spaces of abstract functions.
Math. Nachrichten 155 (1992), 127-140.
Approximation of non-linear parabolic boundary control problems by the
Fourier method
- convergence of optimal controls.
Optimization 22
(1991), 83-98.
On the semigroup approach for the optimal control of semilinear parabolic
equations including
distributed and boundary control.
Z. f. Analysis und
Anwendungen (ZAA) 8 (1989), 431-443.
(with H. Goldberg)
Second order sufficient optimality conditions for a class of control problems
governed by non-linear integral equations with application to parabolic
boundary control.
Optimization 20 (1989), 6871-698.
On a numerical method for coercive parabolic boundary control problems.
Z. Angewandte Mathematik und Mechanik (ZAMM) 67 (1987), 129-135.
(with T. Kaiser)
An inverse problem of parameter identification in cooling
lines.
Wiss. Z. TU Karl-Marx-Stadt 29 (1987), 212-218.
(with W. Sperber)
Function spaces and Lagrange multiplier rules for a parabolic
control problem
arising from the hydration of concrete.
Discussiones Mathematicae
8 (1986), 109-120.
(with J. Ester)
On generalized notions of efficiency in multicriteria programming
problems.
Systems Analysis Modelling Simulation 3 (1986), 153-161.
(with K. Eppler)
On switching points of optimal controls for coercive parabolic
boundary control problems.
Optimization 17 (1986), 93-101.
On changing the spaces in Lagrange multiplier rules for the optimal
control of non-linear
operator equations.
Optimization 16 (1985), 877-885.
On duality and the maximum principle for continuous linear programming
problems.
Z. f. Analysis und Anwendungen (ZAA) 4 (1985), 525-535.
The generalized bang-bang-principle and the numerical solution of a
parabolic boundary-control
problem with constraints on the control
and the state.
ZAMM 64 (1984), 551-557.
A modification of the Zowe and Kurcyusz regularity condition with
application to the
optimal control of Noether operator equations with
constraints on the control and the state.
Math. Operationsforschung und
Statistik 14 (1983), 238-245.
On generalized bang-bang principles for two time-optimal heating problems
with constraints
on the control and the state.
Demonstratio Mathematica
15 (1982), 131-143.
On some parabolic boundary control problems with constraints on the control
and
functional-constraints on the state.
Z. für Analysis und Anwendungen
(ZAA) 17 (1982), 1-13.
Optimalitätsbedingungen für ein parabolisches Randsteuerproblem mit Steuer- und
Zustandsbeschränkungen.
Math. Operationsforschung und
Statistik, Ser. Optimization, 12 (1981), 513-523.
Zur Dualitätstheorie linearer stetiger Optimierungsaufgaben mit Fredholmscher
Operatorbeschränkung erster Art.
Beiträge zur Analysis 17 (1981), 99-112.
Duality theorems for a class of continuous linear programming problems in a
space of
Bochner-integrable abstract functions.
Math. Operationsforschung und
Statistik, 11 (1981), 513-523.
A generalized bang-bang-principle for a heating problem with
constraints on the control and the thermal stress.
J. of Integral Equations 3
(1981), 345-355.
(with A. Hensel and L. v. Wolfersdorf)
Berechnung der Abkühlung von Feinstahl und Draht in Kühlstrecken.
Neue Hütte 25 (1980), 299-301.
Mathematische Untersuchungen zur Auslegung und Steuerung von
Kühlstrecken für Stabstahl- und Drahtwalzwerke.
Neue Hütte,
25 (1980), 384-386.
A minimum principle and a generalized bang-bang-principle for a
distributed optimal control problem
with constraints on the control and
the state.
ZAMM 59 (1979), 737-739.
Dual existence theorems for a special class of linear programming
problems in reflexive Banach lattices.
Math. Operationsforschung und
Statistik 8 (1977), 471-483.
Existenz- und Dualitätsaussagen für lineare Optimierungsaufgaben in reflexiven
Banachräumen.
Math. Operationsforschung
und Statistik 6 (1975), 901-912.