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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

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 $${\mathbb{R}^n}$$ , 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. Copyright Springer-Verlag 2008
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Suggested Citation

  • CHARES, Robert & GLINEUR, François, 2009. "An interior-point method for the single-facility location problem with mixed norms using a conic formulation," LIDAM Reprints CORE 2078, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:2078
    DOI: 10.1007/s00186-008-0225-x
    Note: In : Mathematical Methods of Operations Research, 68, 383-405, 2008
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    1. repec:cor:louvrp:-1726 is not listed on IDEAS
    2. NESTEROV, Yu., 2006. "Towards nonsymmetric conic optimization," LIDAM Discussion Papers CORE 2006028, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. 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.
    4. 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.
    5. 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.
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