Technical Note—Minisum I p Distance Location Problems Solved via a Perturbed Problem and Weiszfeld's Algorithm

James G. Morris and William A. Verdini
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James G. Morris: University of Wisconsin, Madison, Wisconsin
William A. Verdini: Arizona State University, Tempe, Arizona

Operations Research, 1979, vol. 27, issue 6, 1180-1188

Abstract: The classical iterative algorithm originally proposed by Weiszfeld for solving minisum facility location problems is generalized to the case of I p distances. A differentiate approximating function is used to replace the original nondifferentiable convex objective function. The approximating function is shown to be uniformly convergent to the original objective function as a smoothing constant approaches zero. Characterizations and convergence properties peculiar to the algorithm are discussed, and computational experience is presented. The straightforward extension to multifacility location problems is also developed.

Date: 1979
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