An efficient algorithm for the Euclidean r-centrum location problem

An efficient algorithm for the Euclidean r-centrum location problem

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Article ID: iaor2007564
Country: Netherlands
Volume: 167
Issue: 1
Start Page Number: 716
End Page Number: 728
Publication Date: Aug 2005
Journal: Applied Mathematics and Computation
Authors: ,
Keywords: -centre problem
Abstract:

In this paper we consider the single-facility Euclidean r-centrum location problem in ℝn, which generalizes and unifies the classical 1-center and 1-median problem. Specifically, we reformulate this problem as a nonsmooth optimization problem only involving the maximum function, and then develop a smoothing algorithm that is shown to be globally convergent. The method transforms the original nonsmooth problem with certain combinatorial property into the solution of a deterministic smooth unconstrained optimization problem. Numerical results are presented for some problems generated randomly, indicating that the algorithm proposed here is extremely efficient for large problems.

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