In applied sciences PDEs model an extensive variety of phenomena. Typically the final goal of simulations is a system which is optimal in a certain sense. For instance optimal control problems identify a control to steer a system towards a desired state. Inverse problems seek PDE parameters which are most consistent with measurements. In these optimization problems PDEs appear as equality const...

Optimization problems in PDE models are often approached by considering the PDE model as a black-box input-output relation and thus solving an unconstrained optimization problem. In contrast to that, considering the PDE model as a side condition of a resulting constrained programming problem enables us to simultaneously solve the PDE model equations together with the optimization problem. This ...

Optimization problems with constraints which require the solution of a partial differential equation arise widely in many areas of the sciences and engineering, in particular in problems of design. The solution of such PDEconstrained optimization problems is usually a major computational task. Here we consider simple problems of this type: distributed control problems in which the 2and 3-dimens...

The optimization and control of systems governed by partial differential equations (PDEs) usually requires numerous evaluations of the forward problem or the optimality system. Despite the fact that many recent efforts, many of which are reported in this book, have been made to limit or reduce the number of evaluations to 5–10, this cannot be achieved in all situations and even if this is possi...

We develop an adaptive finite element concept for elliptic optimal control problems with constraints on the state. In order to generate goal–oriented meshes, we extend the Dual Weighted Residual (DWR) concept proposed by Becker and Rannacher [1] for PDE-constrained optimization to the state constrained case. Using the optimality system of the underlying PDE-constrained optimal control problem w...