On the Regularity of Generalized Conjugate Functions
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866910105504579584 |
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| author | Oikonomidis, Konstantinos Laude, Emanuel Patrinos, Panagiotis |
| author_facet | Oikonomidis, Konstantinos Laude, Emanuel Patrinos, Panagiotis |
| contents | We investigate regularity properties of generalized conjugate functions induced by a general coupling function and the associated generalized proximal mapping. Our main results provide verifiable conditions ensuring local single-valuedness, continuity, Lipschitz continuity, and differentiability of the generalized proximal mapping, and transfer these properties to generalized conjugates providing explicit derivative formulas. These results are based on a nonsmooth implicit function theorem for generalized equations, relying on graphical localizations and second-order variational tools. Beyond first-order regularity, we also derive conditions under which generalized conjugates are strictly twice differentiable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_04301 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Regularity of Generalized Conjugate Functions Oikonomidis, Konstantinos Laude, Emanuel Patrinos, Panagiotis Optimization and Control We investigate regularity properties of generalized conjugate functions induced by a general coupling function and the associated generalized proximal mapping. Our main results provide verifiable conditions ensuring local single-valuedness, continuity, Lipschitz continuity, and differentiability of the generalized proximal mapping, and transfer these properties to generalized conjugates providing explicit derivative formulas. These results are based on a nonsmooth implicit function theorem for generalized equations, relying on graphical localizations and second-order variational tools. Beyond first-order regularity, we also derive conditions under which generalized conjugates are strictly twice differentiable. |
| title | On the Regularity of Generalized Conjugate Functions |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2604.04301 |