Friday, 16:15 - 16:40 h, Room: MA 415


Matthias Heinkenschloss
A trust-region based adaptive stochastic collocation method for PDE constrained optimization with uncertain coefficients


Many optimization problems in engineering and science are governed by partial differential equations (PDEs) with uncertain parameters. Although such problems can be formulated as optimization problems in Banach spaces and derivative based optimization methods can in principle be applied, the numerical solution of these problems is more challenging than the solution of deterministic PDE constrained optimization problems. The difficulty is that the PDE solution is a random field and the numerical solution of the PDE requires a discretization of the PDE in space/time as well as in the random variables. As a consequence, these optimization problems are substantially larger than the already large deterministic PDE constrained optimization problems.
In this talk we discuss the numerical solution of such optimization problems using stochastic collocation methods. We explore the structure of this method in gradient and Hessian computations. We use a trust-region framework to adapt the collocation points based on the progress of the algorithms and structure of the problem. Convergence results are presented. Numerical results demonstrate significant savings of our adaptive approach.


Talk 3 of the invited session Fri.3.MA 415
"PDE constrained optimization with uncertain data" [...]
Cluster 19
"PDE-constrained optimization & multi-level/multi-grid methods" [...]


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