Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (3): 827-836.

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Characterizations of Farkas Lemmas for a Class of Fractional Optimization with DC Functions

Xinyi Feng(),Xiangkai Sun*()   

  1. Chongqing Key Laboratory of Social Economy and Applied Statistics, College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067
  • Received:2020-06-14 Online:2021-06-26 Published:2021-06-09
  • Contact: Xiangkai Sun;
  • Supported by:
    the NSF of Chongqing(cstc2020jcyj-msxmX0016);the Open Research Platform of CTBU(KFJJ2019097);the Project of CTBU(ZDPTTD201908);the Education Committee Project Foundation of Chongqing for Bayu Young Scholar


This paper deals with some new Farkas lemmas for a class of constraint fractional optimization with DC functions(the difference of convex functions). Following the idea due to Dinkelbach, we first associate the fractional optimization with a DC optimization problem. Then, by using the epigraph technique of the conjugate function, we introduce some new regularity conditions and establish the duality between the DC optimization problem and its Fenchel-Lagrange dual problem. Finally, we obtain some new Farkas lemmas for the fractional optimization problem. Furthermore, we also show that the results obtained in this paper extend and improve the corresponding results in the literature.

Key words: Fractional optimization, Regularity conditions, Farkas lemmas

CLC Number: 

  • O221.2