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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.18377 |
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| _version_ | 1866913405656367104 |
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| author | Van Hien, Le |
| author_facet | Van Hien, Le |
| contents | In this paper, we first establish a formula for exactly computing the regular coderivative of the metric projection operator onto closed balls $r\mathbb{B}$ centered at the origin in Hilbert spaces. Then, this result is extended to metric projection operator onto any closed balls $\mathbb{B}(c,r)$, which has center $c$ in Hilbert space $H$ and with radius $r > 0$. Finally, we give the formula for calculating the graphical derivative of the metric projection operator onto closed balls with center at arbitrarily given point in Hilbert spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_18377 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Regular Coderivative and Graphical Derivative of the Metric Projection onto closed Balls in Hilbert spaces Van Hien, Le Functional Analysis In this paper, we first establish a formula for exactly computing the regular coderivative of the metric projection operator onto closed balls $r\mathbb{B}$ centered at the origin in Hilbert spaces. Then, this result is extended to metric projection operator onto any closed balls $\mathbb{B}(c,r)$, which has center $c$ in Hilbert space $H$ and with radius $r > 0$. Finally, we give the formula for calculating the graphical derivative of the metric projection operator onto closed balls with center at arbitrarily given point in Hilbert spaces. |
| title | Regular Coderivative and Graphical Derivative of the Metric Projection onto closed Balls in Hilbert spaces |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2406.18377 |