A generalization of the rectangular bounding method for continuous location models

We develop a generalized bounding method for the Weiszfeld iterative procedure used to solve the hyperbolically approximated ℓp-norm single- and multifacility minimum location problems. We also show that, at optimality, the solution to the bound problem coincides with the solution to the original location problem. We use this result to show that the rectangular bound value converges to the single-facility location problem optimal objective function value.