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Minimizing sums and products of linear fractional functions over a polytope

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  • Hiroshi Konno
  • Hajime Yamashita

Abstract

In this paper, we develop efficient deterministic algorithms for globally minimizing the sum and the product of several linear fractional functions over a polytope. We will show that an elaborate implementation of an outer approximation algorithm applied to the master problem generated by a parametric transformation of the objective function serves as an efficient method for calculating global minima of these nonconvex minimization problems if the number of linear fractional terms in the objective function is less than four or five. It will be shown that the Charnes–Cooper transformation plays an essential role in solving these problems. Also a simple bounding technique using linear multiplicative programming techniques has remarkable effects on structured problems. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 583–596, 1999

Suggested Citation

  • Hiroshi Konno & Hajime Yamashita, 1999. "Minimizing sums and products of linear fractional functions over a polytope," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(5), pages 583-596, August.
    • Handle: RePEc:wly:navres:v:46:y:1999:i:5:p:583-596
    DOI: 10.1002/(SICI)1520-6750(199908)46:53.0.CO;2-5
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    References listed on IDEAS

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    1. Siegfried Schaible, 1977. "A note on the sum of a linear and linear‐fractional function," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 24(4), pages 691-693, December.
    2. A. Charnes & W. W. Cooper, 1962. "Programming with linear fractional functionals," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 9(3‐4), pages 181-186, September.
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    Cited by:

    1. Bo Zhang & YueLin Gao & Xia Liu & XiaoLi Huang, 2022. "An Outcome-Space-Based Branch-and-Bound Algorithm for a Class of Sum-of-Fractions Problems," Journal of Optimization Theory and Applications, Springer, vol. 192(3), pages 830-855, March.
    2. Ekta Jain & Kalpana Dahiya & Vanita Verma, 2018. "Integer quadratic fractional programming problems with bounded variables," Annals of Operations Research, Springer, vol. 269(1), pages 269-295, October.

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