一类带DC函数的分式优化的Farkas引理刻画  

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

作　　者：冯欣怡 孙祥凯 Feng Xinyi;Sun Xiangkai(Chongqing Key Laboratory of Social Economy and Applied Statistics,College of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing 400067)

机构地区：[1]重庆工商大学数学与统计学院经济社会应用统计重庆市重点实验室,重庆400067

出　　处：《数学物理学报（A辑）》2021年第3期827-836,共10页Acta Mathematica Scientia

基　　金：重庆市自然科学基金(cstc2020jcyj-msxmX0016);重庆市重点实验室开放课题(KFJJ2019097);重庆工商大学科研团队项目(ZDPTTD201908);重庆市巴渝学者青年学者项目。

摘　　要：该文旨在刻画一类带有DC函数(即两个凸函数的差)的约束分式优化问题的Farkas引理.借助Dinkelbach方法,将该分式优化问题转化为DC优化问题.随后借助共轭函数的上图技巧所引入的新的正则性条件,刻画了该DC优化问题与其Fenchel-Lagrange对偶问题之间的对偶关系,从而建立了该分式优化问题的一些新的Farkas引理,推广和改进了相关文献的结果.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.

关 键 词：分式优化 正则性条件 FARKAS引理 

分 类 号：O221.2[理学—运筹学与控制论]