Topic: Directional differentiability for solution operators of vectorial sweeping processeswith applications in optimal control
 
Abstract: We study directional differentiability properties of solution operators of rate-independent evolution variational inequalitieswith full-dimensional convex polyhedral admissible sets. It is shown that, if the space of continuous functions of bounded variationis used as the domain of definition, then the most prototypical examples of such solution operators - the vector play and stop - areHadamard directionally differentiable in a pointwise manner if and only if the admissible set is non-obtuse. We further prove that,in those cases where they exist, the directional derivatives of the vector play and stop are uniquely characterized by a system ofprojection identities and variational inequalities and that directional differentiability cannot be expected for obtuse polyhedraeven if the solution operator is restricted to the space of Lipschitz continuous functions. The obtained results give rise toBouligand stationarity conditions for optimal control problems governed by sweeping processes and, in the one-dimensional case,to strong stationarity systems that generalize classical results of Mignot.

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