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In this paper we propose a general methodology for solving a broad class ofcontinuous, multifacility location problems, in any dimension and with$\ell_\tau$-norms proposing two different methodologies: 1) by a new secondorder cone mixed integer programming formulation and 2) by formulating asequence of semidefinite programs that converges to the solution of theproblem; each of these relaxed problems solvable with SDP solvers in polynomialtime. We apply dimensionality reductions of the problems by sparsity andsymmetry in order to be able to solve larger problems.

Algorithms and dimensionality reductions for continuous multifacility ordered median location problems