TITLE: Robust shape optimization

ABSTRACT: The motivation for robust optimization comes from the fact that real-world systems often face uncertain-
ties, such as manufacturing tolerances or material variations. These uncertainties can make optimized
designs unreliable if they are not properly considered. Therefore, it’s essential to create designs that
are not only optimal but also robust, meaning they can still perform well even when conditions change
slightly. To robustify against uncertainty we will consider in this talk a minmax problem, where the inner
maximization problem is with respect to the uncertainty. To solve this bilevel problem, we work with
the maximal value functions of the lower-level maximization problems and apply a version of Danskin’s
theorem for the computation of generalized derivatives. A nonsmooth optimization method is used to
solve the outer robust problem. To conclude, we present numerical results for the proposed approach.