Year: 2026
Type: preprint
Abstract: This paper develops specular differentiation for mappings between real normed vector spaces, extending the classical notions of Gâteaux and Fréchet differentiability. These notions apply to a broad class of nonsmooth functions, including functions for which certain other generalized derivatives do not exist. We investigate their fundamental theoretical properties and establish a Quasi-Mean Value Theorem for real-valued functions. Finally, we prove that the specular Gâteaux derivative of a semi-convex functional, whenever it exists at an interior point of its effective domain, determines a global quadratic lower bound and belongs to its Fréchet subdifferential.
Source: arXiv (Cornell University)
Author: Jung, Kiyuob
Institution: Michigan State University
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7124677392
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