Convex Valued Geodesics and Applications to Sweeping Processes with Bounded Retraction

We provide a formulation for sweeping processes with arbitrary locally bounded retraction, not necessarily left or right continuous. Moreover we provide a proof of the existence and uniqueness of solutions for this formulation which relies on the reduction to the 1-Lipschitz continuous case by using a suitable family of geodesics for the asymmetric Hausdorff-like distance called excess.