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

 

Hanne Tiesler
Stochastic collocation for optimal control problems with stochastic PDE constraints

Coauthors: Robert Mike Kirby, Tobias Preusser, Dongbin Xiu

 

Abstract:
The use of stochastic collocation schemes for the solution of optimal control problems, constrained by stochastic partial differential equations (SPDE), is presented. The constraining SPDE depends on random data and accordingly, the randomness will propagate to the states of the system, whereas the control is assumed to be deterministic. There exist different efficient numerical schemes for the solution of SPDEs, one of them is the stochastic collocation method, which is based on the generalized polynomial chaos. For the minimization of the constrained optimization problems we combine the stochastic collocation method with a gradient descent method as well as a sequential quadratic program (SQP). In the presented work, different optimization problems are considered, i.e., we define different objective functions of tracking type to show different application possibilities. The functions involve several higher order moments of the random states as well as classical regularization of the control. The developed methods are compared to the widely used Monte Carlo method. Numerical results illustrate the performance of the new optimization approach with stochastic collocation.

 

Talk 1 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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