New Characterizations of Nonsmooth Convex Functions via Generalized Derivatives
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866908914391449600 |
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| author | Phat, Vo Thanh |
| author_facet | Phat, Vo Thanh |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_24951 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | New Characterizations of Nonsmooth Convex Functions via Generalized Derivatives Phat, Vo Thanh Optimization and Control 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. |
| title | New Characterizations of Nonsmooth Convex Functions via Generalized Derivatives |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2603.24951 |