A primal algorithm for the weighted minimum covering ball problem in $$\mathbb {R}^n$$ R n

P. M. Dearing (), Pietro Belotti () and Andrea M. Smith
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P. M. Dearing: Clemson University
Pietro Belotti: Xpress Optimization team
Andrea M. Smith: Liberty University

TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, 2016, vol. 24, issue 2, No 11, 466-492

Abstract: Abstract The nonlinear programming problem of finding the minimum covering ball of a finite set of points in $$\mathbb {R}^n$$ R n , with a positive weight corresponding to each point, is solved by a directional search method. At each iteration, the search path is either a ray or the arc of a circle and is determined by bisectors of points. Each step size along the search path is determined explicitly. The primal algorithm is shown to search along the farthest point Voronoi diagram of the given points. We provide computational results that show the efficiency of the algorithm when compared to general convex nonlinear optimization solvers.

Keywords: Minimum covering ball; One-center location; Min–max location; Nonlinear programming; Voronoi diagram; 90B80 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s11750-015-0405-9

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