复合优化问题的ε-对偶间隙性质和ε-强对偶

doi:10.13438/j.cnki.jdzk.2020.03.002

吉首大学学报（自然科学版）

复合优化问题的ε-对偶间隙性质和ε-强对偶

田利萍，方东辉

(吉首大学数学与统计学院，湖南吉首 416000)

出版日期:2020-03-25 发布日期:2020-12-13
通讯作者: 方东辉(1979—),男,湖南洞口人，吉首大学数学与统计学院教授,博士,主要从事最优化理论研究.
基金资助:
国家自然科学基金资助项目(11861033)；湖南省教育厅科研项目（17A172）

Characterization of ε-Duality Gap Properties and ε-Strong Duality for Composite Optimization Problems

TIAN Liping, FANG Donghui

(College of Mathematics and Statistics, Jishou University, Jishou 416000, Hunan China)

Online:2020-03-25 Published:2020-12-13

摘要/Abstract

摘要：

利用共轭函数的上图性质,并引入2类新的约束规范条件,等价刻画了复合优化问题与其Lagrange对偶问题之间的ε-对偶间隙性质、εε-强对偶和ε-Farkas引理.

关键词： 复合优化, &epsilon, -对偶间隙性质, &epsilon, -强对偶；&epsilon, -Farkas引理

Abstract:

By using the epigraph technique of conjugate functions, we give two new constraint qualifications. With these constraint qualifications, ε-duality gap properties, ε-strong duality and ε-Farkas lemma between composite optimization problem and its Lagrange dual problem are established.

Key words: composite optimization; ε-duality gap properties, ε-strong duality, ε-Farkas lemma

田利萍，方东辉. 复合优化问题的ε-对偶间隙性质和ε-强对偶[J]. 吉首大学学报（自然科学版）, DOI: 10.13438/j.cnki.jdzk.2020.03.002.

TIAN Liping, FANG Donghui. Characterization of ε-Duality Gap Properties and ε-Strong Duality for Composite Optimization Problems[J]. Journal of Jishou University（Natural Sciences Edition), DOI: 10.13438/j.cnki.jdzk.2020.03.002.

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复合优化问题的ε-对偶间隙性质和ε-强对偶

Characterization of ε-Duality Gap Properties and ε-Strong Duality for Composite Optimization Problems

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