一类带DC函数的分式优化的Farkas引理刻画

数学物理学报 ›› 2021, Vol. 41 ›› Issue (3): 827-836.

一类带DC函数的分式优化的Farkas引理刻画

冯欣怡(),孙祥凯*()

^{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}

收稿日期:2020-06-14 出版日期:2021-06-26 发布日期:2021-06-09
通讯作者: 孙祥凯 E-mail:1518684363@qq.com;sxkcqu@163.com
作者简介:冯欣怡, E-mail: 1518684363@qq.com
基金资助:
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

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

Xinyi Feng(),Xiangkai Sun*()

^{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 E-mail:1518684363@qq.com;sxkcqu@163.com
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

摘要/Abstract

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.

关键词: 分式优化, 正则性条件, Farkas引理

Abstract:

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

中图分类号:

O221.2

冯欣怡,孙祥凯. 一类带DC函数的分式优化的Farkas引理刻画[J]. 数学物理学报, 2021, 41(3): 827-836.

Xinyi Feng,Xiangkai Sun. Characterizations of Farkas Lemmas for a Class of Fractional Optimization with DC Functions[J]. Acta mathematica scientia,Series A, 2021, 41(3): 827-836.

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