DC复合优化问题的最优性条件

数学物理学报 ›› 2021, Vol. 41 ›› Issue (4): 1079-1087.

DC复合优化问题的最优性条件

胡玲莉(),田利萍(),方东辉*()

^{吉首大学数学与统计学院湖南吉首 416000}

收稿日期:2020-09-29 出版日期:2021-08-26 发布日期:2021-08-09
通讯作者: 方东辉 E-mail:847285225@qq.com;tianliping6889@163.com;fang@jsu.edu.cn
作者简介:胡玲莉, E-mail: 847285225@qq.com|田利萍, E-mail: tianliping6889@163.com
基金资助:
国家自然科学基金(11861033);湖南省自然科学基金(2020JJ4494);吉首大学科研基金(Jd20008);吉首大学科研基金(Jd20009)

Optimality Conditions for DC Composite Optimization Problems with Conical Constraints

Lingli Hu(),Liping Tian(),Donghui Fang*()

^{College of Mathematics and Statistics, Jishou University, Hunan Jishou 416000}

Received:2020-09-29 Online:2021-08-26 Published:2021-08-09
Contact: Donghui Fang E-mail:847285225@qq.com;tianliping6889@163.com;fang@jsu.edu.cn
Supported by:
the NSFC(11861033);the NSF of Hunan Province(2020JJ4494);the Scientific Research Fund of Jishou University(Jd20008);the Scientific Research Fund of Jishou University(Jd20009)

摘要/Abstract

摘要：

该文在函数不一定下半连续，集合不一定闭的情形下，利用凸化技术，定义了DC复合优化问题的对偶问题，建立了DC复合优化问题的最优性条件和最优解的鞍点刻画，推广了已有的相关结论.

关键词: DC复合优化问题, 最优性条件, 鞍点定理

Abstract:

In the case when the functions are not necessarily lower semicontinuous and the sets are not necessarily closed, we first define the dual problem for DC composite optimization problems with conical constraints by using convexification technique, then some optimality conditions and saddle point theorems are obtained, which extend the corresponding results in the previous papers.

Key words: DC composite optimization problem, Optimality condition, Saddle point theorem

中图分类号:

O221.2

胡玲莉,田利萍,方东辉. DC复合优化问题的最优性条件[J]. 数学物理学报, 2021, 41(4): 1079-1087.

Lingli Hu,Liping Tian,Donghui Fang. Optimality Conditions for DC Composite Optimization Problems with Conical Constraints[J]. Acta mathematica scientia,Series A, 2021, 41(4): 1079-1087.

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