Computation of graphical derivatives of normal cone maps to a class of conic constraint sets

Abstract

This paper concerns with the graphical derivative of the normals to the conic constraint $g(x)\in\!K$, where $g\!:\mathbb{X}\to\mathbb{Y}$ is a twice continuously differentiable mapping and $K\subseteq\mathbb{Y}$ is a nonempty closed convex set assumed to be $C^2$-cone reducible. Such a generalized derivative plays a crucial role in characterizing isolated calmness of the solution maps to generalized equations whose multivalued parts are modeled via the normals to the nonconvex set $\Gamma=g^{-1}(K)$. The main contribution of this paper is to provide an exact characterization for the graphical derivative of the normals to this class of nonconvex conic constraints under an assumption without requiring the nondegeneracy of the reference point as the papers \cite{Gfrerer17,Mordu15,Mordu151} do.