New Characterizations of Nonsmooth Convex Functions via Generalized Derivatives
Optimization and Control
2026-03-27 v1
Abstract
This paper studies the convexity properties of nonsmooth extended-real-valued weakly convex functions, a class of functions that is central to modern optimization and its applications. We establish new characterizations of convexity using second-order generalized derivative tools, including subgradient graphical derivatives, second subderivatives, and second-order subdifferentials. These tools allow us to derive necessary and sufficient conditions for convexity in the nonsmooth framework.
Keywords
Cite
@article{arxiv.2603.24951,
title = {New Characterizations of Nonsmooth Convex Functions via Generalized Derivatives},
author = {Vo Thanh Phat},
journal= {arXiv preprint arXiv:2603.24951},
year = {2026}
}