Grégoire Allaire (Paris)
Linearized approach to worst-case design in shape otimization.
In this joint work with Charles Dapogny, we propose a deterministic method for optimizing a structure with respect
to its worst possible behavior when a `small' uncertainty exists over some of its features. The main idea
of the method is to linearize the considered cost function with respect to the uncertain parameters, then
to consider the supremum function of the obtained linear approximation, which can be rewritten as a more
classical function of the design, owing to standard adjoint techniques from optimal control theory. The
resulting "linearized worst-case" objective function turns out to be the sum of the initial cost function and of
a norm of an adjoint state function, which is dual with respect to the considered norm over perturbations.
This formal approach is very general, and can be justified in some special cases. In particular, it allows to
address several problems of considerable importance in both parametric and shape optimization of elastic
structures, in a unified framework.
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