The Stable Farkas Lemma for Composite Convex Functions in Infinite Dimensional Spaces

被引:10
作者
Li, Gang [1 ]
Zhou, Yu-ying [2 ]
机构
[1] Zhejiang Agr & Forestry Univ, Sch Sci, Hangzhou 311300, Zhejiang, Peoples R China
[2] Soochow Univ, Dept Math, Suzhou 215006, Peoples R China
关键词
conjugate functions; epigraph; stable Farkas lemma; stable duality; OPTIMALITY CONDITIONS; OPTIMIZATION; DUALITY; REGULARITY; FORMULA;
D O I
10.1007/s10255-015-0493-1
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we consider a general composite convex optimization problem with a cone-convex system in locally convex Hausdorff topological vector spaces. Some Fenchel conjugate transforms for the composite convex functions are derived to obtain the equivalent condition of the Stable Farkas Lemma, which is formulated by using the epigraph of the conjugates for the convex functions involved and turns out to be weaker than the classic Slater condition. Moreover, we get some necessary and sufficient conditions for stable duality results of the composite convex functions and present an example to illustrate that the monotonic increasing property of the outer convex function in the objective function is essential. Our main results in this paper develop some recently results.
引用
收藏
页码:677 / 692
页数:16
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