The main focus of this paper is on an a-posteriori analysis for the method of proper orthogonal decomposition (POD) applied to optimal control problems governed by
parabolic and elliptic PDEs. Based on a perturbation method it is deduced how far the suboptimal
control, computed on the basis of the POD model, is from the (unknown)
exact one. Numerical examples illustrate the realization of the proposed approach for linear-quadratic problems governed by parabolic and elliptic partial differential equations.
The paper introduces an identification problem arising in modern regional hyperthermia, a cancer
therapy aiming at heating the tumor by microwave radiation. The task is to identify the highly
individual perfusion, which affects the resulting temperature distribution, from MR measurements.
The identification problem is formulated as an optimization problem. Existence of a solution and
optimality conditions are analyzed. Different regularizations and problem variants are considered. For
the numerical solution, a standard SQP method is used. Sufficient conditions for the convergence of
the method are derived. Finally, numerical examples on artificial as well as clinical data are presented.