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Newton’s Method for the Ellipsoidal lp Norm Facility Location Problem

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3991)

Abstract

We give the minisum ellipsoidal l p norm facility location model. Our model includes both p≥ 2 and p<2 cases. We derive the optimality conditions for our model and transform the optimality conditions into a system of equations. We then solve the system by perturbed Newton’s method. Some numerical examples are presented.

Keywords

Demand Point Nonmonotone Line Search Road Distance Complementarity Function Global Minimal Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Dennis Jr., J.E., Schnabel, R.B.: Numerical methods for unconstrained optimization and nonlinear equations. Prentice Hall Series in Computational Mathematics. Prentice Hall Inc., Englewood Cliffs (1983)MATHGoogle Scholar
  2. 2.
    Fernández, J., Fernández, P., Pelegrin, B.: Estimating actual distances by norm functions: a comparison between the l k,p,θ-norm and the \(l_{b_1,b_2,\theta}\)-norm and a study about the selection of the data set. Comput. Oper. Res. 29(6), 609–623 (2002)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Love, R.F., Morris, J.G.: Modelling inter-city road distances by mathematical functions. Operational Research Quarterly 23, 61–71 (1972)MATHCrossRefGoogle Scholar
  4. 4.
    Love, R.F., Morris, J.G.: Mathematical models of road travel distances. Management Science 25, 130–139 (1979)MATHCrossRefGoogle Scholar
  5. 5.
    Love, R.F.: The dual of a hyperbolic approximation to the generalized constrained multi-facility location problem with l p distances. Management Sci 21(1), 22–33 (1974)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Tyrrell Rockafellar, R.: Convex analysis. Princeton Mathematical Series, vol. 28. Princeton University Press, Princeton (1970)MATHGoogle Scholar
  7. 7.
    Xia, Y.: An algorithm for perturbed second-order cone programs. Technical Report AdvOl-Report No. 2004/17, McMaster University (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Yu Xia
    • 1
  1. 1.The Institute of Statistical MathematicsTokyoJapan

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