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Minimization of the sum of three linear fractional functions

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Abstract

In this paper, we will propose an efficient and reliable heuristic algorithm for minimizing and maximizing the sum of three linear fractional functions over a polytope. These problems are typical nonconvex minimization problems of practical as well as theoretical importance. This algorithm uses a primal-dual parametric simplex algorithm to solve a subproblem in which the value of one linear function is fixed. A subdivision scheme is employed in the space of this linear function to obtain an approximate optimal solution of the original problem. It turns out that this algorithm is much more efficient and usually generates a better solution than existing algorithms. Also, we will develop a similar algorithm for minimizing the product of three linear fractional functions.

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Authors and Affiliations

  1. Department of Industrial Engineering and Management, Tokyo Institute of Technology, Japan

    Hiroshi Konno

  2. Arthur Anderson Co., Japan

    Natsuroh Abe

Authors
  1. Hiroshi Konno
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  2. Natsuroh Abe
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Konno, H., Abe, N. Minimization of the sum of three linear fractional functions. Journal of Global Optimization 15, 419–432 (1999). https://doi.org/10.1023/A:1008376731013

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  • DOI: https://doi.org/10.1023/A:1008376731013

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