On the Coderivative of the Projection Operator onto the Positive Cone in Hilbert spaces

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 co...

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Bibliographic Details
Published inarXiv.org
Main Authors Le Van Hien, Nguyen, Viet Quan
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 10.07.2024
Subjects
Euclidean geometry
Hilbert space
Operators (mathematics)
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Summary: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 \(l_2\).
ISSN:2331-8422