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

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  • CHARES, Robert
  • GLINEUR, François

    (Université catholique de Louvain (UCL). Center for Operations Research and Econometrics (CORE))

Abstract

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 R, 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 a given accuracy. Finally, we report computational results for this algorithm and compare with standard nonlinear optimization solvers applied to this problem.

Suggested Citation

  • CHARES, Robert & GLINEUR, François, 2007. "An interior-point method for the single-facility location problem with mixed norms using a conic formulation," LIDAM Discussion Papers CORE 2007071, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2007071
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    References listed on IDEAS

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    1. repec:cor:louvrp:-1726 is not listed on IDEAS
    2. F. Glineur & T. Terlaky, 2004. "Conic Formulation for l p -Norm Optimization," Journal of Optimization Theory and Applications, Springer, vol. 122(2), pages 285-307, August.
    3. François Glineur, 2001. "Proving Strong Duality for Geometric Optimization Using a Conic Formulation," Annals of Operations Research, Springer, vol. 105(1), pages 155-184, July.
    4. Yu. E. Nesterov & M. J. Todd, 1997. "Self-Scaled Barriers and Interior-Point Methods for Convex Programming," Mathematics of Operations Research, INFORMS, vol. 22(1), pages 1-42, February.
    5. NESTEROV, Yu., 2006. "Towards nonsymmetric conic optimization," LIDAM Discussion Papers CORE 2006028, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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