Wednesday, 15:45 - 16:10 h, Room: MA 004

 

Adrian Sichau
Shape optimization under uncertainty employing a second order approximation for the robust counterpart

Coauthor: Stefan Ulbrich

 

Abstract:
We present a second order approximation for the robust counterpart of general uncertain NLP with state equation given by a PDE. We show how the approximated worst-case functions, which are the essential part of the approximated robust counterpart, can be formulated as trust-region problems that can be solved efficiently. Also, the gradients of the approximated worst-case functions can be computed efficiently combining a sensitivity and an adjoint approach. However, there might be points where these functions are nondifferentiable. Hence, we introduce an equivalent formulation of the approximated robust counterpart (as MPEC), in which the objective and all constraints are differentiable. This formulation can further be extended to model the presence of actuators that are capable of applying forces to a structure in order to counteract the effects of uncertainty. The method is applied to shape optimization in structural mechanics to obtain optimal solutions that are robust with respect to uncertainty in acting forces and material parameters. Numerical results are presented.

 

Talk 2 of the contributed session Wed.3.MA 004
"Applications of robust optimization V" [...]
Cluster 20
"Robust optimization" [...]

 

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