Nearest points to closed sets and directional derivatives of distance functions

DOI10.1017/S0004972700002707zbMath0674.46011MaRDI QIDQ3828513

Simon Fitzpatrick

Publication date: 1989

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

directional derivativesmetric projectionnearest pointsone-sided derivatives of the distance function

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)

Related Items

Subdifferentials of distance function outside of target set in Riemannian manifolds ⋮ Derivatives of generalized farthest functions and existence of generalized farthest points ⋮ Porosity of perturbed optimization problems in Banach spaces ⋮ On closures of preimages of metric projection mappings in Hilbert spaces ⋮ Convergence of subdifferentials and normal cones in locally uniformly convex Banach space ⋮ Limiting subdifferentials of perturbed distance functions in Banach spaces ⋮ Subdifferentials of perturbed distance function in Riemannian manifolds ⋮ Generalized derivatives of distance functions and the existence of nearest points ⋮ Derivatives of generalized distance functions and existence of generalized nearest points

Cites Work

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• Weak compactness and reflexivity
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• The Proximal Normal Formula in Banach Space
• A Smooth Variational Principle With Applications to Subdifferentiability and to Differentiability of Convex Functions