Generalized derivatives of distance functions and the existence of nearest points

DOI10.1016/j.na.2008.03.043zbMath1172.46006OpenAlexW2102757529MaRDI QIDQ1006692

Chong Li, Jinsu He

Publication date: 25 March 2009

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2008.03.043

zbMATH Keywords

generalized derivativesdistance functionnearest pointsproximinal setsapproximatively compact sets

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Applications of functional analysis in optimization, convex analysis, mathematical programming, economics (46N10) Derivatives of functions in infinite-dimensional spaces (46G05)

Cites Work

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• The differentiability of real functions on normed linear space using generalized subgradients
• On the Clarke subdifferential of the distance function of a closed set
• Derivatives of generalized distance functions and existence of generalized nearest points
• On some geometric properties of suns
• A distance function property implying differentiability
• Differentiability of the distance function and points of multi-valuedness of the metric projection in Banach space
• Differentiation of Real-Valued Functions and Continuity of Metric Projections
• Nearest points to closed sets and directional derivatives of distance functions
• Metric projections and the differentiability of distance functions

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