Mordukhovich Derivatives of Metric Projection Operator in Hilbert Spaces

In this paper, we study the generalized differentiability of the metric projection operator in Hilbert spaces. We find exact expressions for Mordukhovich derivatives (which are also called Mordukhovich coderivatives) for the metric projection operator onto closed balls in Hilbert spaces and positive...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 203; no. 3; pp. 2649 - 2678
Main Author: Li, Jinlu
Format: Journal Article
Language:English
Published: New York Springer US 01.12.2024
Springer Nature B.V
Subjects:
Applications of Mathematics
Approximation
Banach spaces
Calculus of Variations and Optimal Control; Optimization
Closed balls
Codes
Engineering
Euclidean geometry
Hilbert space
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Operators (mathematics)
Optimization
Theory of Computation
46C05
Strict Fréchet derivative
Mordukhovich derivative
Fréchet derivative
90C25
Metric projection operator
Gâteaux directional derivative
65K10
49M27
47H05
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary:In this paper, we study the generalized differentiability of the metric projection operator in Hilbert spaces. We find exact expressions for Mordukhovich derivatives (which are also called Mordukhovich coderivatives) for the metric projection operator onto closed balls in Hilbert spaces and positive cones in Euclidean spaces and in real Hilbert space l 2 . We investigate the connection between Frèchet derivatives, Gâteaux directional derivatives and the Mordukhovich derivatives of the metric projection in Hilbert spaces.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-024-02530-2