An interior-point method for the single-facility location problem with mixed norms using a conic formulation

  • Robert Chares
  • François Glineur
Original Article


We consider the single-facility location problem with mixed norms, i.e. the problem of minimizing the sum of the distances from a point to a set of fixed points in \({\mathbb{R}^n}\) , where each distance can be measured according to a different p-norm. We show how this problem can be expressed into a structured conic format by decomposing the nonlinear components of the objective into a series of constraints involving three-dimensional cones. Using the availability of a self-concordant barrier for these cones, we present a polynomial-time algorithm (a long-step path-following interior-point scheme) to solve the problem up to any given accuracy. Finally, we report computational results for this algorithm and compare with standard nonlinear optimization solvers applied to this problem.


Nonsymmetric conic optimization Conic reformulation Sum of norm minimization Single-facility location problems Interior-point methods 


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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Center for Operations Research and Econometrics (CORE)Université catholique de Louvain (UCL)Louvain-la-NeuveBelgium

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