Multigrid for optimization solvers
Volker Schulz (Uni Trier)
Multigrid methods are solution strategies for discretized PDE
of lowest computational complexity. In particular, this problem class
includes also saddle-point-type problems like the Stokes equation.
In this talk, we demonstrate that these methods can be profitably
used also within solution routines for model based optimization
problems, where the model consists of PDE.
On the one hand, of course, multigrid methods can be employed for
the solution of linearized model equations within an optimization
routine with advantage. On the other hand, the whole optimization
procedure can be reformulated in a form appropriate for the
application of multigrid methods -- in a similar style like
multigrid methods are used for Stokes problems. The saddle point
problems arising in the latter approach, however, differ
significantly from the variational-type saddle point problems
In this talk, we give a survey on various possibilities
for using multigrid methods for the solution of
optimization problems and demonstrate their practical usability.