鲁棒复合优化问题的Lagrange对偶

数学物理学报 ›› 2020, Vol. 40 ›› Issue (4): 1095-1107.

鲁棒复合优化问题的Lagrange对偶

叶冬平(),方东辉*()

^{吉首大学数学与统计学院湖南吉首 416000}

收稿日期:2019-07-23 出版日期:2020-08-26 发布日期:2020-08-20
通讯作者: 方东辉 E-mail:1441638656@qq.com;dh_fang@jsu.edu.cn
作者简介:叶冬平, E-mail:1441638656@qq.com
基金资助:
国家自然科学基金(11861033);湖南省自然科学基金(2020JJ4494);湖南省教育厅科研项目(17A172);吉首大学校级科研项目(Jdy19001)

Lagrange Dualities for Robust Composite Optimization Problems

Dongping Ye(),Donghui Fang*()

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

Received:2019-07-23 Online:2020-08-26 Published:2020-08-20
Contact: Donghui Fang E-mail:1441638656@qq.com;dh_fang@jsu.edu.cn
Supported by:
the NSFC(11861033);the NSF of Hunan Province(2020JJ4494);the Scientific Research Fund of Hunan Provincial Education Department(17A172);the Scientific Research Fund of Jishou University(Jdy19001)

摘要/Abstract

摘要：

利用共轭函数的上图性质，引入两类新的约束规范条件，等价刻画了鲁棒复合优化问题与其对偶问题之间的Lagrange零对偶，强对偶，稳定零对偶及稳定强对偶，推广和改进了前人的相关结论.

关键词: 鲁棒复合优化问题, 约束规范条件, 零对偶, 强对偶

Abstract:

By using the properties of the epigraph of the conjugate functions, two new constraint qualifications are given. Under these constraint qualifications, the zero duality, the strong duality, the stable zero duality and the stable strong duality between robust composite optimization problem and its Lagrange dual problems are established, which extend and improve the corresponding results in the previous papers.

Key words: Robust composite optimization problem, Constraint qualification, Zero duality, Strong duality

中图分类号:

O224

叶冬平,方东辉. 鲁棒复合优化问题的Lagrange对偶[J]. 数学物理学报, 2020, 40(4): 1095-1107.

Dongping Ye,Donghui Fang. Lagrange Dualities for Robust Composite Optimization Problems[J]. Acta mathematica scientia,Series A, 2020, 40(4): 1095-1107.

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