On inner calmness*, generalized calculus, and derivatives of the normal cone mapping

In this paper, we study continuity and Lipschitzian properties of set-valued mappings, focusing on inner-type conditions. We introduce new notions inner calmness* and, its relaxation, fuzzy calmness*. show that polyhedral maps enjoy examine (fuzzy) a multiplier mapping associated with constraint systems in depth. Then utilize these to develop some rules generalized differential calculus, mainly for the primal objects (e.g. tangent cones). particular, propose an exact chain rule graphical derivatives. apply results compute derivatives normal cone mapping, essential e.g. sensitivity analysis variational inequalities.