Farkas-type results for constrained fractional programming with DC functions
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In this paper, by using the properties of the epigraph of the conjugate functions, we introduce some closedness conditions and investigate some characterizations of these closedness conditions. Then, by using these closedness conditions, we obtain some Farkas-type results for a constrained fractional programming problem with DC functions. We also show that our results encompass as special cases some programming problems considered in the recent literature.
KeywordsClosedness conditions Farkas-type results Fractional programming DC functions
The authors would like to thank the Editor and the two anonymous Referees for valuable comments and suggestions, which helped to improve the paper. Research of the first author was partially supported by the National Natural Science Foundation of China (Grant No: 11301570), the Basic and Advanced Research Project of CQ CSTC (Grant No: cstc2013jcyjA00003), the China Postdoctoral Science Foundation funded project (Grant No: 2013M540697) and the Research Fund of Chongqing Technology and Business University (Grant No: 2013-56-03). Research of the second author was partially supported by the National Natural Science Foundation of China (Grant No: 61374135). Research of the third author was partially supported by the Natural Science Foundation Project of CQ CSTC (Grant No: cstc2012jjA00038).
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