Seminario di analisi numerica
ore
10:00
presso - Aula Da Stabilire -
We address the solution of PDE-constrained optimal control problems
via semismooth Newton methods. Specifically, we consider problems
with control constraints and with nonsmooth costs that are known to
promote sparse optimal controls, i.e. controls which are identically
zero on large parts of the control domain [HSW].
A typical example is the L$^1$ cost that has been used, e.g., for the
optimal placement of control devices [S].
Following a discretize-then-optimize approach, we analyze the convergence
properties of the Newton method applied to the discretization of optimal
control problems with nonsmooth regularization terms.
Moreover, we present the study of the impact
of the control sparsity on the structure of the arising linear systems
and propose preconditioners which exploit this information.
Numerical experiments on 3D problems are presented