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

  • Authors:

  • Takahito Kuno;Toshiyuki Masaki

  • Affiliations:

  • Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba, Japan 305-8573;Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba, Japan 305-8573

  • Venue:
  • Computational Optimization and Applications
  • Year:
  • 2013

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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.