Stable and Total Fenchel Duality for Composed Convex Optimization Problems

被引：7
|
作者：
Fang, Dong-hui [1 ]
Wang, Xian-yun [1 ]
机构：
[1] Jishou Univ, Coll Math & Stat, Jishou 416000, Peoples R China
来源：
ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES | 2018年 / 34卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Composed convex optimization problem; constraint qualifications; strong duality; total duality; CONSTRAINT QUALIFICATIONS; PROGRAMS; OPTIMALITY; SPACES;
D O I：
10.1007/s10255-018-0793-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider the composed convex 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 and the subdifferentials of convex functions, we give some new constraint qualifications which completely characterize the strong Fenchel duality and the total Fenchel duality for composed convex optimiztion problem in real locally convex Hausdorff topological vector spaces.
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页码：813 / 827
页数：15
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