Constructions of solutions to generalized Sylvester and Fermat-Torricelli problems for Euclidean balls

DOI10.1007/s10957-013-0366-9zbMath1318.90073arXiv1210.3142OpenAlexW2015169153MaRDI QIDQ2251551

Nguyen Mau Nam, Nguyen Thai An, Nguyen Dinh Hoang

Publication date: 14 July 2014

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.3142

zbMATH Keywords

optimizationconvex analysisgeneralized differentiationFermat-Torricelli problemsmallest enclosing circle problem

Mathematics Subject Classification ID

Minimax problems in mathematical programming (90C47) Convex functions and convex programs in convex geometry (52A41) Convexity of real functions of several variables, generalizations (26B25) Euclidean geometries (general) and generalizations (51M05) Euclidean analytic geometry (51N20)

Related Items (3)

A proximal method for solving nonlinear minmax location problems with perturbed minimal time functions via conjugate duality ⋮ Minsum location extended to gauges and to convex sets ⋮ A dual simplex-type algorithm for the smallest enclosing ball of balls

Cites Work

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• The Fermat-Torricelli problem. I: A discrete gradient-method approach
• Minimal enclosing discs, circumcircles, and circumcenters in normed planes. I.
• Minimal enclosing discs, circumcircles, and circumcenters in normed planes. II.
• Applications of variational analysis to a generalized Fermat-Torricelli problem
• An extension of the Fermat-Torricelli problem
• Convex analysis and nonlinear optimization. Theory and examples.
• On the smallest enclosing balls
• On the point for which the sum of the distances to \(n\) given points is minimum
• Geometric methods and optimization problems
• The Fermat--Torricelli problem in normed planes and spaces
• Minimal time functions and the smallest intersecting ball problem with unbounded dynamics
• On the geometry of the smallest circle enclosing a finite set of points
• Constrained optimization and image space analysis. Vol. 1: Separation of sets and optimality conditions
• A Generalized Sylvester Problem and a Generalized Fermat-Torricelli Problem
• Applications of Convex Analysis to the Smallest Intersecting Ball Problem
• APPROXIMATING SMALLEST ENCLOSING BALLS WITH APPLICATIONS TO MACHINE LEARNING
• A Look at the Generalized Heron Problem through the Lens of Majorization-Minimization
• Convex Analysis

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