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Some dual characterizations of Farkas-type results for fractional programming problems

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Abstract

In this paper, we present some Farkas-type results for a fractional programming problem. To this end, by using the properties of dualizing parametrization functions, Lagrangian functions and the epigraph of the conjugate functions, we introduce some new notions of regularity conditions and then obtain some dual forms of Farkas-type results for this fractional programming problem. We also obtain sufficient conditions for alternative type theorems. As an application of these results, we obtain the corresponding results for a convex optimization problem.

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Acknowledgements

This research was supported by the Basic and Advanced Research Project of CQ CSTC (cstc2017jcyjBX0032, cstc2015jcyjB00001, cstc2016jcyjA0178, cstc2016jcyjA1296, cstc2015jcyjA00009), the National Natural Science Foundation of China (11401058, 11471059, 11626048, 11701057), the Program for University Innovation Team of Chongqing (CXTDX201601026), the Education committee Project Foundation of Bayu Scholar, and the Education Committee Project Research Foundation of Chongqing (KJ1500628).

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Authors and Affiliations

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

    Xiangkai Sun, Liping Tang & Xian-Jun Long

  2. School of Mathematics and Finance, Chongqing University of Arts and Sciences, Chongqing, 402160, China

    Minghua Li

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  1. Xiangkai Sun
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  2. Liping Tang
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  3. Xian-Jun Long
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  4. Minghua Li
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Correspondence to Xiangkai Sun.

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Sun, X., Tang, L., Long, XJ. et al. Some dual characterizations of Farkas-type results for fractional programming problems. Optim Lett 12, 1403–1420 (2018). https://doi.org/10.1007/s11590-017-1196-8

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