Strict Frechet Differentiability of the Metric Projection Operator in Hilbert Spaces
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866914780054290432 |
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| author | Li, Jinlu |
| author_facet | Li, Jinlu |
| contents | In this paper, we prove strict Frechet differentiability of the metric projection operator onto closed balls in Hilbert spaces and onto positive cones in Euclidean spaces. We find the exact expressions for Frechet derivatives. Since Frechet differentiability implies Gateaux directional differentiability, the results obtained in this paper strengthen the results obtained in [8] and [10] about the directional differentiability of the metric projection operator onto closed balls in Hilbert spaces and positive cones in Euclidean spaces and in the real Hilbert space l2. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_14362 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Strict Frechet Differentiability of the Metric Projection Operator in Hilbert Spaces Li, Jinlu Functional Analysis In this paper, we prove strict Frechet differentiability of the metric projection operator onto closed balls in Hilbert spaces and onto positive cones in Euclidean spaces. We find the exact expressions for Frechet derivatives. Since Frechet differentiability implies Gateaux directional differentiability, the results obtained in this paper strengthen the results obtained in [8] and [10] about the directional differentiability of the metric projection operator onto closed balls in Hilbert spaces and positive cones in Euclidean spaces and in the real Hilbert space l2. |
| title | Strict Frechet Differentiability of the Metric Projection Operator in Hilbert Spaces |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2312.14362 |