Lower Semicontinuous Regularization for Vector-Valued Mappings

被引:0
|
作者
M. Ait Mansour
A. Metrane
M. Théra
机构
[1] Faculté des Sciences et Techniques LACO – UMR 6090,
[2] GERAD,undefined
来源
Journal of Global Optimization | 2006年 / 35卷
关键词
D.C.-mappings; lower level set; lower semicontinuous regularization; vector lower limit; vector-valued mappings; Primary 47A15; Secondary 46A32; 47D20;
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学科分类号
摘要
The paper is devoted to studying the lower semicontinuity of vector-valued mappings. The main object under consideration is the lower limit. We first introduce a new definition of an adequate concept of lower and upper level sets and establish some of their topological and geometrical properties. A characterization of semicontinuity for vector-valued mappings is thereafter presented. Then, we define a concept of vector lower limit, proving its lower semicontinuity, and furnishing in this way a concept of lower semicontinuous regularization for mappings taking their values in a complete lattice. The results obtained in the present work subsume the standard ones when the target space is finite dimensional. In particular, we recapture the scalar case with a new flexible proof. In addition, extensions of usual operations of lower and upper limits for vector-valued mappings are explored. The main result is finally applied to obtain a continuous D.C. decomposition of continuous D.C. mappings.
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页码:283 / 309
页数:26
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