On Characterizations of (Almost) Strictly Convex Functions
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918486326902784 |
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| author | Bauschke, Heinz H. Luo, Honglin Wang, Xianfu |
| author_facet | Bauschke, Heinz H. Luo, Honglin Wang, Xianfu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_05147 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Characterizations of (Almost) Strictly Convex Functions Bauschke, Heinz H. Luo, Honglin Wang, Xianfu Classical Analysis and ODEs Functional Analysis Optimization and Control 52A41, 49H05 (Primary) 26B25, 90C25 (Secondary) 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. |
| title | On Characterizations of (Almost) Strictly Convex Functions |
| topic | Classical Analysis and ODEs Functional Analysis Optimization and Control 52A41, 49H05 (Primary) 26B25, 90C25 (Secondary) |
| url | https://arxiv.org/abs/2605.05147 |