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复合凸优化问题的Fenchel-Lagrange强对偶之研究 被引量：1

Strong Fenchel-Lagrange Duality for Convex Optimization Problems with Composite Function
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摘要 利用共轭函数的上图性质,引入新的约束规范条件,等价刻画了目标函数为凸函数与凸复合函数之和的复合优化问题及其Fenchel-Lagrange对偶问题之间的强对偶与稳定强对偶. In this paper,we consider a convex composite optimization problem which consists in minimizing the sum of a convex function and a convex composite function.By using the properties of the epigraph of the conjugate functions,some sufficient and necessary conditions for the strong and stable strong Fenchel-Lagrange dualities are provided.
作者 方东辉 田利萍 王仙云 Fang Donghui;Tian Liping;Wang Xianyun(College of Mathematics and Statistics,Jishou University,Hunan Jishou 416000)
机构地区 吉首大学数学与统计学院
出处 《数学物理学报（A辑）》 CSCD 北大核心 2020年第1期20-30,共11页 Acta Mathematica Scientia
基金 国家自然科学基金(11861033) 湖南省教育厅科研基金(17A172)。
关键词 Fenchel-Lagrange强对偶 约束规范条件 复合凸优化问题 Fenchel-Lagrange duality Constraint qualification Convex composite optimization problem
分类号 O224 [理学—运筹学与控制论]
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数学物理学报（A辑）
2020年 第1期

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