带锥约束的复合优化问题的最优性条件

数学物理学报 ›› 2018, Vol. 38 ›› Issue (6): 1112-1121.

带锥约束的复合优化问题的最优性条件

胡玲莉(),方东辉*()

吉首大学数学与统计学院湖南吉首 416000

收稿日期:2017-12-06 出版日期:2018-12-26 发布日期:2018-12-27
通讯作者: 方东辉 E-mail:847285225@qq.com;dh_fang@jsu.edu.cn
作者简介:胡玲莉, E-mail: 847285225@qq.com
基金资助:
国家自然科学基金(11461027);湖南省自然科学基金(2016JJ2099);湖南省教育厅科研基金(17A172)

Optimality Conditions for Composite Optimization Problems with Conical Constraints

Lingli Hu(),Donghui Fang*()

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

Received:2017-12-06 Online:2018-12-26 Published:2018-12-27
Contact: Donghui Fang E-mail:847285225@qq.com;dh_fang@jsu.edu.cn
Supported by:
the NSFC(11461027);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：

利用函数的次微分性质，通过引进新的约束规范条件，等价刻画了带锥约束的复合优化问题的最优性条件和对应的Lagrange函数的鞍点定理，推广了前人的相关结论.

关键词: 复合优化, 最优性条件, 鞍点, 锥优化

Abstract:

By using the properties of subdifferentials, some new constraint qualifications are obtained, which characterize completely some optimality conditions for composite optimization problem with conical constraints. Moreover, saddle point theorems for the Lagrange function of this optimization problem are also given. Our results extend the corresponding results in the previous papers.

Key words: Composite optimization problem, Optimality condition, Saddle point, Conic programming

中图分类号:

O221.2

胡玲莉, 方东辉. 带锥约束的复合优化问题的最优性条件[J]. 数学物理学报, 2018, 38(6): 1112-1121.

Lingli Hu, Donghui Fang. Optimality Conditions for Composite Optimization Problems with Conical Constraints[J]. Acta mathematica scientia,Series A, 2018, 38(6): 1112-1121.

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