On well-posed mutually nearest and mutually furthest point problems in Banach spaces

DOI10.1007/s10114-003-0287-xzbMath1069.46010OpenAlexW2049778175MaRDI QIDQ1888710

Chong Li, Ren-Xing Ni

Publication date: 26 November 2004

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-003-0287-x

zbMATH Keywords

Hausdorff metricfarthest pointsnearest pointsgeneric existence results

Mathematics Subject Classification ID

Set-valued and variational analysis (49J53) 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)

Related Items (5)

Porosity of Mutually Nearest and Mutually Furthest Points Problems in Geodesic Space ⋮ Derivatives of generalized farthest functions and existence of generalized farthest points ⋮ Existence and porosity for a class of perturbed optimization problems in Banach spaces ⋮ Nearest and farthest points in spaces of curvature bounded below ⋮ Characterizations and Uniqueness of Mutually Nearest Points for Two Sets in Normed Spaces

Cites Work

• Well-posed optimization problems
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• Geometry of Banach spaces. Selected topics
• Farthest points in weakly compact sets
• Almost Chebyshev set with respect to bounded subsets
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• Farthest points of sets in uniformly convex Banach spaces
• Support and distance functionals for convex sets
• Existence Of Nearest Points In Banach Spaces
• Metric projections and the differentiability of distance functions
• Porous Sets in Best Approximation Theory
• Convex Optimization and the Epi-Distance Topology
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