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

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Detalles Bibliográficos
Autores principales:	Van Hien, Le, Quan, Nguyen Viet
Formato:	Preprint
Publicado:	2024
Materias:	Functional Analysis
Acceso en línea:	Acceder al recurso
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_version_	1866907974922928128
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

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