Fenchel duality in infinite-dimensional setting and its applications

被引：17

作者：

Ng, KF

Song, W ^{[1
]}

机构：

[1] Harbin Normal Univ, Dept Math, Harbin 150080, Peoples R China

[2] Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2003年 / 55卷 / 7-8期

关键词：

Fenchel duality; convex optimization; polyhedron; the strong conical hull intersection property;

D O I：

10.1016/j.na.2003.07.008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study Fenchel duality problems, in infinite-dimensional spaces, that involve the minimizing of a sum of two proper convex functions, where one of which is polyhedral. We use a constraint qualification with the notion of the strong quasi-interior of a convex set, and then deduce duality results and subgradient formula. As applications, we discuss the strong conical hull intersection property of convex sets. Finally, by using a duality result due to Rodriques and Simons, we establish several duality results for convex optimization over a finite intersection of closed convex sets. (C) 2003 Elsevier Ltd. All rights reserved.

引用

页码：845 / 858

页数：14

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