邻近映射在Bregman度量下的推广

Generalization of Proximal Mapping under Bregman Distance

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。

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.