The Optimal Smoothings of Sublinear Functions and Convex Cones
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866915455546949632 |
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| author | Samakhoana, Thabo Grimmer, Benjamin |
| author_facet | Samakhoana, Thabo Grimmer, Benjamin |
| contents | This paper considers the problem of smoothing convex functions and sets, seeking the nearest smooth convex function or set to a given one. For convex cones and sublinear functions, a full characterization of the set of all optimal smoothings is given. These provide if and only if characterizations of the set of optimal smoothings for any target level of smoothness. Optimal smoothings restricting to either inner or outer approximations also follow from our theory. Finally, we apply our theory to provide insights into smoothing amenable functions given by compositions with sublinear functions and generic convex sets by expressing them as conic sections. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_06681 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Optimal Smoothings of Sublinear Functions and Convex Cones Samakhoana, Thabo Grimmer, Benjamin Optimization and Control This paper considers the problem of smoothing convex functions and sets, seeking the nearest smooth convex function or set to a given one. For convex cones and sublinear functions, a full characterization of the set of all optimal smoothings is given. These provide if and only if characterizations of the set of optimal smoothings for any target level of smoothness. Optimal smoothings restricting to either inner or outer approximations also follow from our theory. Finally, we apply our theory to provide insights into smoothing amenable functions given by compositions with sublinear functions and generic convex sets by expressing them as conic sections. |
| title | The Optimal Smoothings of Sublinear Functions and Convex Cones |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2508.06681 |