| 摘要: |
| 针对N维欧式空间中的邻近映射，将范数推广为更为一般的Bregman度量，研究了在Bregman度量意义下邻近映射的基本性质，得出了在什么条件下Bregman-邻近映射是单点集，对于定理的结论给出了一个具体的例子，并在Bregman度量意义下对第二邻近映射定理进行了推广;运用指示函数δC，得到一个集合的投影和临近映射之间的等价关系。 |
| 关键词: 邻近映射 Bregman度量 投影 凸函数 |
| DOI： |
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| 基金项目: |
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| Generalization of Proximal Mapping under Bregman Distance |
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MO Fan
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| Abstract: |
| For the proximal mappings in n-dimensional Euclidean spaces, the norm is generalized to a more general Bregman distance. The basic properties of the proximal mappings in the sense of Bregman m distance are studied. Under what conditions the proximal mappings are a singleton. A concrete example is given for the conclusion of the theorem and generalization of the second proximal mapping theorem under Bregman distance. By using a special indicator function δc, the equivalent relation between the orthogonal projection of a set and the adjacent mapping is obtained. |
| Key words: proximal mapping Bregman distance projection convex function |
