Convergence of the Weiszfeld Algorithm for Weber Problems Using a Generalized “Distance” Function

This paper considers a generalization of the single and multisource Weber problem for the case when the “distance” function is some power K of the usual I_p distance. Properties of the generalized problem are established, and an appropriate generalization of the Weiszfeld iterative approach is given. A convergence proof is supplied for an ϵ-approximation to the original problem, under certain restrictions on p and K.