Derivatives of generalized distance functions and existence of generalized nearest points

DOI10.1006/jath.2001.3651zbMath1006.46015OpenAlexW2101116900MaRDI QIDQ1599250

Chong Li, Ren-Xing Ni

Publication date: 12 March 2003

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jath.2001.3651

zbMATH Keywords

Minkowski functionaldirectional derivativescompactly locally uniformly convexgeneralized distance functiongeneralized nearest pointstrictly convex and Kadeč set

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20)

Related Items (13)

Derivatives of generalized farthest functions and existence of generalized farthest points ⋮ Convexity of generalized proximinal sets in Banach spaces ⋮ On generalized simultaneous nearest point in normed spaces ⋮ Infimal convolution and optimal time control problem. II: Limiting subdifferential ⋮ Infimal convolution and optimal time control problem. I: Fréchet and proximal subdifferentials ⋮ Secure multi-party convex hull protocol based on quantum homomorphic encryption ⋮ Exact characterization for subdifferentials of a special optimal value function ⋮ Limiting subgradients of minimal time functions in Banach spaces ⋮ The representation and continuity of a generalized metric projection onto a closed hyperplane in Banach spaces ⋮ Subdifferentials of a minimum time function in Banach spaces ⋮ Generalized derivatives of distance functions and the existence of nearest points ⋮ Anisotropic best τ_C -approximation in normed spaces ⋮ Characterizations of generalized proximinal subspaces in real Banach spaces

Cites Work

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• The nearest point mapping is single valued nearly everywhere
• On the Clarke subdifferential of the distance function of a closed set
• On a generalized best approximation problem
• On well posed generalized best approximation problems
• 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
• Existence Of Nearest Points In Banach Spaces
• Nearest points to closed sets and directional derivatives of distance functions
• Metric projections and the differentiability of distance functions
• Porous Sets in Best Approximation Theory

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