Abstract:
Primal-dual interior-point methods have proven to be very
efficient in the context of large scale nonlinear programming.
In this talk, we present a convergence analysis of a primal-dual
interior-point method for PDE-constrained optimization in an
appropriate function space setting. Considered are optimal
control problems with control constraints in . It is shown
that the developed primal-dual interior-point method converges
globally and locally superlinearly. Not only the
-setting
is analyzed, but also a more involved
-analysis,
,
is presented.
In
, the set of feasible controls contains interior points
and the Fréchet differentiability of the perturbed optimality
system can be shown. In the
-setting, which is highly relevant
for PDE-constrained optimization, these nice properties are no
longer available. Nevertheless, using refined techniques, a
convergence analysis can be carried out. In particular, two-norm
techniques and a smoothing step are required. Numerical results are
presented.
This seminar is easily accessible to persons with disabilities. For more information or for assistance, please contact the Mathematics Department at 743-3500.