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

Computational Optimization and Applications volume 54, pages93–109(2013)Cite this article

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.

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Affiliations

  1. Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba, Ibaraki, 305-8573, Japan

    Takahito Kuno & Toshiyuki Masaki

Authors
  1. Takahito Kuno
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  2. Toshiyuki Masaki
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Corresponding author

Correspondence to Takahito Kuno.

Additional information

T. Kuno was partially supported by a Grant-in-Aid for Challenging Exploratory Research (22651057) from the Japan Society for the Promotion of Sciences.

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Kuno, T., Masaki, T. A practical but rigorous approach to sum-of-ratios optimization in geometric applications. Comput Optim Appl 54, 93–109 (2013). https://doi.org/10.1007/s10589-012-9488-5

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Keywords

  • Global optimization
  • Sum-of-ratios optimization
  • Branch-and-bound
  • Computer vision
  • Multiple-view geometry