[Dottorcomp] Seminari di Matematica Applicata, 09/09/2025, Tommaso Vanzan

[Stefano Lisini]

Seminari di Matematica Applicata, Dipartimento di Matematica "F. Casorati"
e Istituto del CNR IMATI "E. Magenes" di Pavia.

Martedì 9 Settembre 2025, alle ore 15 precise, presso la sala conferenze
dell'IMATI-CNR di Pavia,

Tommaso Vanzan (Politecnico di Torino)
terrà un seminario dal titolo:

Multilevel methods and fast linear solvers for PDE-constrained optimization
under uncertainty.

Abstract: In recent years there has been an increasing interest in
optimization problems constrained by random partial differential equations,
since the latter are effective mathematical tools to take into account
intrinsic randomness or partial knowledge of systems under study.

The solution of such problems requires an extremely high computational
cost, and thus motivates a very active area of research.
In particular, the use of multilevel/sparse techniques is not trivial in
this context, since a direct multilevel/sparse approximation of the
objective functional involves negative weights, which may eventually lead
to a loss of convexity.

In the first part of the talk, we present a novel framework to use
multilevel and sparse quadrature formulae, that still preserves the
properties (e.g., convexity) of the continuous problem. Our approach
consists in solving a sequence of optimization problems, each discretized
with different levels of accuracy of the physical and probability spaces.
The final approximation of the minimizer is obtained in a post-processing
step, by suitably combining the adjoint variables computed on the different
levels.

In the second part, I will give an overview of selected contributions to
fast inner solvers tailored for the extremely large KKT systems, based on
algebraic, operator preconditioning and multigrid strategies.

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https://matematica.unipv.it/ricerca/cicli-di-seminari/seminari-di-matematica-applicata/