Numerical Analysis for PDE-constrained Optimal Control Problems
Contact: Prof. Dr. I. Neitzel
Time: Monday 12:15-13:45 and Tuesday 8:30-10:00
Room: 5.002 (Wegeler Str. 6).
Exams during the second examination period will be held on Tuesday, March 29th. Please contact Ms Oberheim by March 17th to schedule an appointment.
We will discuss questions arising in the numerical analysis of optimal control problems subject to (linear and possibly semilinear) partial differential equations and additional inequality constraints on the control and/or the state. Our main focus is on deriving a priori error estimates for the finite element discretization of such problems. Depending on the participants' background in partial differential equations, optimal control theory, and numerical analysis of PDEs, we will develop the theoretical background such as existence and regularity of optimal solutions, necessary and sufficient optimality conditions, and in the case of pointwise state constraints also regularization strategies. We will discuss different discretization strategies and derive rates of convergence for the discrete optimal controls.
- Fredi Tröltzsch. Optimale Steuerung partieller Differentialgleichungen, Vieweg+Teubner 2009
- Michal Hinze, Rene Pinnau, Michael Ulbrich, Stefan Ulbrich. Optimization with PDE constraints. Mathematical Modelling: Theory and Applications, 23. Springer, 2009.(Chapter 4)
- Dietrich Braess. Finite Elemente. Springer
- Michael Hinze. A variational discretization concept in control constrained optimization: the linear quadratic case. Comput. Optim. Appl. 30 (2005), no. 1, 45-61
- Arnd Rösch. Error estimates for linear-quadratic control problems with control constraints. Optim. Methods Softw. 21 (2006), no. 1, 121-134.
- Eduardo Casas and Fredi Trötzsch. Error estimates for the finite element approximation of a semilinear elliptic control problem. Control and Cybernetics 31 (2002), 695-712.
- Christian Meyer. Error estimates for the finite element approximation of an elliptic control problem with pointwise state and control constraints. Control and Cybernetics 37, 2008. no.1, 51-83
- Klaus Deckelnick and Michael Hinze. Convergence of a finite element approximation to a state-constrained elliptic control problem. SIAM J. Numer. Anal. 45, 2007, no.3, 335-350