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

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  • Takahito Kuno
  • Toshiyuki Masaki

Abstract

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

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    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.
    2. H. P. Benson, 2002. "Global Optimization Algorithm for the Nonlinear Sum of Ratios Problem," Journal of Optimization Theory and Applications, Springer, vol. 112(1), pages 1-29, January.
    3. Danny Z. Chen & Ovidiu Daescu & Yang Dai & Naoki Katoh & Xiaodong Wu & Jinhui Xu, 2005. "Efficient Algorithms and Implementations for Optimizing the Sum of Linear Fractional Functions, with Applications," Journal of Combinatorial Optimization, Springer, vol. 9(1), pages 69-90, February.
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    Cited by:

    1. Hongwei Jiao & Binbin Li & Wenqiang Yang, 2024. "A criterion-space branch-reduction-bound algorithm for solving generalized multiplicative problems," Journal of Global Optimization, Springer, vol. 89(3), pages 597-632, July.
    2. Jiao, Hongwei & Ma, Junqiao, 2022. "An efficient algorithm and complexity result for solving the sum of general affine ratios problem," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    3. Shen, Peiping & Zhu, Zeyi & Chen, Xiao, 2019. "A practicable contraction approach for the sum of the generalized polynomial ratios problem," European Journal of Operational Research, Elsevier, vol. 278(1), pages 36-48.

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