带复合函数的分式优化问题的Farkas引理

数学物理学报 ›› 2018, Vol. 38 ›› Issue (5): 842-854.

带复合函数的分式优化问题的Farkas引理

方东辉*(),刘伟玲()

吉首大学数学与统计学院湖南吉首 416000

收稿日期:2017-07-25 出版日期:2018-11-09 发布日期:2018-11-09
通讯作者: 方东辉 E-mail:dh_fang@jsu.edu.cn;761481687@qq.com
作者简介:刘伟玲, E-mail:761481687@qq.com
基金资助:
国家自然科学基金(11461047);湖南省自然科学基金(2016JJ2099);湖南省教育厅科研基金(17A172)

The Farkas Lemmas for Fractional Optimization Problem with Composite Functions

Donghui Fang*(),Weilin Liu()

College of Mathematics and Statistics, Jishou University, Hunan Jishou 416000

Received:2017-07-25 Online:2018-11-09 Published:2018-11-09
Contact: Donghui Fang E-mail:dh_fang@jsu.edu.cn;761481687@qq.com
Supported by:
the NSFC(11461047);the Hunan Provincial National Natural Science Foundation of China(2016JJ2099);the Scientific Research Fund of Hunan Provincial Education Department(17A172)

摘要/Abstract

摘要：

借助Dinkelbach的方法（见文献[1]），将带复合函数的分式优化问题转化为约束优化问题.通过引入新的约束规范条件，建立了约束优化问题的对偶理论，进而刻画了带复合函数的分式优化问题的Farkas类引理.

关键词: 分式优化问题, 复合函数, 约束规范条件, Farkas引理

Abstract:

In this paper, the fractional optimization problem with composite functions is turned into a constraint optimization problem by using the previous method. By introducing some news constraint qualifications, some duality results for the constraint optimization problem are established and some Farkas type lemmas for the fractional optimization problem with composite functions are then given.

Key words: Fractional optimization problem, Composite function, Constraint qualification, Frakas lemma

中图分类号:

O221.2

方东辉,刘伟玲. 带复合函数的分式优化问题的Farkas引理[J]. 数学物理学报, 2018, 38(5): 842-854.

Donghui Fang,Weilin Liu. The Farkas Lemmas for Fractional Optimization Problem with Composite Functions[J]. Acta mathematica scientia,Series A, 2018, 38(5): 842-854.

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