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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.08007 |
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| _version_ | 1866907974922928128 |
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| author | Van Hien, Le Quan, Nguyen Viet |
| author_facet | Van Hien, Le Quan, Nguyen Viet |
| contents | In this paper, we study the generalized differentiability of the metric projection operator onto the positive cone in Hilbert spaces. We first establish the formula for exactly computing the regular coderivative and the Mordukhovich coderivative of the metric projection operator onto the positive cone in Euclidean spaces. Then, these results are also established for the projection operator onto the positive cone in the real Hilbert space $l_2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_08007 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Coderivative of the Projection Operator onto the Positive Cone in Hilbert spaces Van Hien, Le Quan, Nguyen Viet Functional Analysis In this paper, we study the generalized differentiability of the metric projection operator onto the positive cone in Hilbert spaces. We first establish the formula for exactly computing the regular coderivative and the Mordukhovich coderivative of the metric projection operator onto the positive cone in Euclidean spaces. Then, these results are also established for the projection operator onto the positive cone in the real Hilbert space $l_2$. |
| title | On the Coderivative of the Projection Operator onto the Positive Cone in Hilbert spaces |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2407.08007 |