  This paper presents a first continuous, linear, conic formulation for the
Discrete Ordered Median Problem (DOMP). Starting from a binary, quadratic
formulation in the original space of location and allocation variables that are
common in Location Analysis (L.A.), we prove that there exists a transformation
of that formulation, using the same space of variables, that allows us to cast
DOMP as a continuous linear problem in the space of completely positive
matrices. This is the first positive result that states equivalence between the
family of continuous convex problems and some hard problems in L.A. The result
is of theoretical interest because it allows us to share the tools from
continuous optimization to shed new light into the difficult combinatorial
structure of the class of ordered median problems.
