On Characterizations of (Almost) Strictly Convex Functions
Classical Analysis and ODEs
2026-05-07 v1 Functional Analysis
Optimization and Control
Abstract
In this paper, we unify and improve existing results on characterizing strict and almost stricty convex functions via subdifferential mapping, Moreau envelope, and proximal mappings. In particular, it is shown that if a convex function is subdifferentiable on its domain, then it is strictly convex if and only if its subdifferential is strictly monotone, equivalently, almost strictly monotone. Rockafellar-Wets' characterizations of almost strictly convex functions via almost differentiability of Fenchel conjugates and strict monotonicity of subdifferentials are extended from a finite-dimensional space to a Hilbert space. We also establish similar results for paramonotone operators.
Cite
@article{arxiv.2605.05147,
title = {On Characterizations of (Almost) Strictly Convex Functions},
author = {Heinz H. Bauschke and Honglin Luo and Xianfu Wang},
journal= {arXiv preprint arXiv:2605.05147},
year = {2026}
}