  This paper addresses the general continuous single facility location problems
in finite dimension spaces under possibly different $\ell_p$ norms in the
demand points. We analyze the difficulty of this family of problems and revisit
convergence properties of some well-known algorithms. The ultimate goal is to
provide a common approach to solve the family of continuous $\ell_p$ ordered
median location problems in dimension $d$ (including of course the $\ell_p$
minisum or Fermat-Weber location problem for any $p\ge 1$). We prove that this
approach has a polynomial worse case complexity for monotone lambda weights and
can be also applied to constrained and even non-convex problems.
