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

arXiv: https://arxiv.org/abs/1709.05592 · HTML: https://mlsanity.com/paper/1709.05592/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Sep 2017.

## Built on by (most cited first, 1 of 1)

- [dOPT: Differentiating Conic Optimization via Geometric Reduction](https://mlsanity.com/paper/2609.33828/) (2026)

## Abstract (arXiv)

This paper concerns with the graphical derivative of the normals to the conic constraint g(x)∈!K, where g!:mathbbX→mathbbY is a twice continuously differentiable mapping and KsubseteqmathbbY is a nonempty closed convex set assumed to be C2-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 citeGfrerer17,Mordu15,Mordu151 do.