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On robust duality for fractional programming with uncertainty data

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Abstract

In this paper, we present a duality theory for fractional programming problems in the face of data uncertainty via robust optimization. By employing conjugate analysis, we establish robust strong duality for an uncertain fractional programming problem and its uncertain Wolfe dual programming problem by showing strong duality between the deterministic counterparts: robust counterpart of the primal model and the optimistic counterpart of its dual problem. We show that our results encompass as special cases some programming problems considered in the recent literature. Moreover, we also show that robust strong duality always holds for linear fractional programming problems under scenario data uncertainty or constraint-wise interval uncertainty, and that the optimistic counterpart of the dual is tractable computationally.

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Acknowledgments

We would like to express our sincere thanks to the anonymous referee for many helpful comments and constructive suggestions which have contributed to the final preparation of this paper.

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Authors and Affiliations

  1. College of Automation, Chongqing University, Chongqing, 400044, China

    Xiang -Kai Sun & Yi Chai

  2. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, China

    Xiang -Kai Sun

  3. State Key Laboratory of Power Transmission Equipment and System Security and New Technology, Chongqing University, Chongqing, 400044, China

    Yi Chai

Authors
  1. Xiang -Kai Sun
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  2. Yi Chai
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Correspondence to Xiang -Kai Sun.

Additional information

This research was partially supported by the National Natural Science Foundation of China (Grant numbers: 11171362 and 11201509).

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Sun, X.K., Chai, Y. On robust duality for fractional programming with uncertainty data. Positivity 18, 9–28 (2014). https://doi.org/10.1007/s11117-013-0227-7

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