Optimizing ordered median functions with applications to single facility location

  • Victor Blanco
  • Justo Puerto
  • Safae El Haj Ben Ali
Conference paper
Part of the Operations Research Proceedings book series (ORP)


This paper considers the problem of minimizing the ordered median function of finitely many rational functions over compact semi-algebraic sets. Ordered median of rational functions are not, in general, neither rational functions nor the supremum of rational functions.We prove that the problem can be transformed into a new problem embedded in a higher dimension space where it admits a convenient representation. This reformulation admits a hierarchy of SDP relaxations that approximates, up to any degree of accuracy, the optimal value of those problems. We apply this general framework to a broad family of continuous location problems solving some difficult problems.


Rational Function Demand Point Ordered Weight Average Median Function Convenient Representation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Victor Blanco
    • 1
  • Justo Puerto
    • 2
  • Safae El Haj Ben Ali
    • 2
  1. 1.Dep. of AlgebraUniversidad de GranadaGranadaSpain
  2. 2.Universidad de Sevilla, IMUSSevillaSpain

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