The Bregman Proximal Average
针对1-强制勒让德函数，定义了布雷格曼近端平均，其布雷格曼包络是各函数布雷格曼包络的凸组合，近端映射也是各函数凸化近端映射的凸组合。
We provide a proximal average with repect to a $1$-coercive Legendre function. In the sense of Bregman distance, the Bregman envelope of the proximal average is a convex combination of Bregman envelopes of individual functions. The Bregman proximal mapping of the average is a convex combination of convexified proximal mappings of individual functions. Techniques from variational analysis provide the keys for the Bregman proximal average.