OS Numerical Optimization: On PDE-constrained optimization under uncertainty: an approximation scheme and solution strategies
Wann
Dienstag, 11. Juli 2023
15:15 bis 16:45 Uhr
Wo
D406
Veranstaltet von
B. Azmi & S. Volkwein
Vortragende Person/Vortragende Personen:
Dr. Tommaso Vanzan
On 11th July 2023 at 15:15, Dr. Tommaso Vanzan from the École Polytechnique Fédérale de Lausanne will give a talk.
In recent years there has been an increasing interest in optimization prob- lems constrained by random Partial Differential Equations (PDEs), since the latter are effective mathematical tools to take into account intrinsic ran- domness or partial knowledge of the system under study.
After an introduction to the topic, we will discuss a new approximation framework tailored to overcome the curse of dimensionality, i.e. to be ef- fective when the random PDE depends on a very large number of random parameters. This new approach, which relies on the combination tech- nique framework, is based on mixed difference of spatial approximations and quadrature formulae for the stochastic variables. It then requires the solution of several optimization problems (which are much cheaper com- pared to a direct fine approximation of the original one). To solve such problems, we then discuss iterative solvers and preconditioners tailored for the linear optimality systems that typically arise in PDE-constrained opti- mization under uncertainty.
The talk is based on a joint work with Fabio Nobile (EPFL).