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

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.