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A practical but rigorous approach to sum-of-ratios optimization in geometric applications


  • Takahito Kuno


  • Toshiyuki Masaki


In this paper, we develop an algorithm for minimizing the L q norm of a vector whose components are linear fractional functions, where q is an arbitrary positive integer. The problem is a kind of sum-of-ratios optimization problem, and often occurs in computer vision. In that case, it is characterized by a large number of ratios and a small number of variables. The algorithm we propose here exploits this feature and generates a globally optimal solution in a practical amount of computational time. Copyright Springer Science+Business Media, LLC 2013

Suggested Citation

  • Takahito Kuno & Toshiyuki Masaki, 2013. "A practical but rigorous approach to sum-of-ratios optimization in geometric applications," Computational Optimization and Applications, Springer, vol. 54(1), pages 93-109, January.
  • Handle: RePEc:spr:coopap:v:54:y:2013:i:1:p:93-109
    DOI: 10.1007/s10589-012-9488-5

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    References listed on IDEAS

    1. James E. Falk & Richard M. Soland, 1969. "An Algorithm for Separable Nonconvex Programming Problems," Management Science, INFORMS, vol. 15(9), pages 550-569, May.
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