Tuesday, 15:45 - 16:10 h, Room: MA 415


Martin Grepl
A certified reduced basis approach for parametrized linear-quadratic optimal control problems

Coauthor: Mark Kärcher


The solution of optimal control problems governed by partial differential equations (PDEs) using classical discretization techniques such as finite elements or finite volumes is computationally very expensive and time-consuming since the PDE must be solved many times. One way of decreasing the computational burden is the surrogate model based approach, where the original high-dimensional model is replaced by its reduced order approximation. However, the solution of the reduced order optimal control problem is suboptimal and reliable error estimation is therefore crucial.
In this talk, we present error estimation procedures for linear-quadratic optimal control problems governed by parametrized parabolic PDEs. To this end, employ the reduced basis method as a surrogate model for the solution of the optimal control problem and develop rigorous and efficiently evaluable a posteriori error bounds for the optimal control and the associated cost functional. Besides serving as a certificate of fidelity for the suboptimal solution, our a posteriori error bounds are also a crucial ingredient in generating the reduced basis with greedy algorithms.


Talk 2 of the invited session Tue.3.MA 415
"Optimization applications in industry II" [...]
Cluster 19
"PDE-constrained optimization & multi-level/multi-grid methods" [...]


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