Optimality Conditions for Elliptic and Parabolic Control Problems
Abstract
In the first part of this talk, we study optimal control problems for
semilinear elliptic control problems subject to control and state constraints.
General boundary conditions are considered and both boundary and distributed
control. The problems are fully discretized and necessary conditions of
optimality are discussed, both for the continuous and the discrete control
problem. It is shown that an interior point code is capable of solving the
resulting NLP problems. Several numerical examples are presented including
cases with singular and bang-bang controls.
Then all the regular elliptic cases and additionally parabolic problems from
the literature, including the instationary Burgers' equation,
are subjected to a postprocessing phase. A general postprocessor
is described which accepts the output of any NLP solver with an AMPL interface
and evaluates the second order sufficient optimality conditions. It allows to
verify numerically that the solutions computed in all cases are local minimizers
of the objective functional.
