New Characterizations of Nonsmooth Convex Functions via Generalized Derivatives

Vo Thanh Phat

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arXiv · 2603.24951

New Characterizations of Nonsmooth Convex Functions via Generalized Derivatives

Vo Thanh Phat

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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.

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Vo Thanh Phat. 2026-03-26. New Characterizations of Nonsmooth Convex Functions via Generalized Derivatives. https://arxiv.org/abs/2603.24951

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