Set-valued evenly convex functions: characterizations and c-conjugacy
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912183110074368 |
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| author | Fajardo, M. D. |
| author_facet | Fajardo, M. D. |
| contents | In this work we deal with set-valued functions with values in the power set of a separated locally convex space where a nontrivial pointed convex cone induces a partial order relation. A set-valued function is evenly convex if its epigraph is an evenly convex set, i.e., it is the intersection of an arbitrary family of open half-spaces. In this paper we characterize evenly convex set-valued functions as the pointwise supremum of its set-valued e-affine minorants. Moreover, a suitable conjugation pattern will be developed for these functions, as well as the counterpart of the biconjugation Fenchel-Moreau theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_06079 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Set-valued evenly convex functions: characterizations and c-conjugacy Fajardo, M. D. Optimization and Control 49N15, 52A41, 90C25 In this work we deal with set-valued functions with values in the power set of a separated locally convex space where a nontrivial pointed convex cone induces a partial order relation. A set-valued function is evenly convex if its epigraph is an evenly convex set, i.e., it is the intersection of an arbitrary family of open half-spaces. In this paper we characterize evenly convex set-valued functions as the pointwise supremum of its set-valued e-affine minorants. Moreover, a suitable conjugation pattern will be developed for these functions, as well as the counterpart of the biconjugation Fenchel-Moreau theorem. |
| title | Set-valued evenly convex functions: characterizations and c-conjugacy |
| topic | Optimization and Control 49N15, 52A41, 90C25 |
| url | https://arxiv.org/abs/2501.06079 |