On subgradient projectors
  The subgradient projector is of considerable importance in convex optimization because it plays the key role in Polyak's seminal work - and the many papers it spawned - on subgradient projection algorithms for solving convex feasibility problems.   In this paper, we offer a systematic study of the subgradient projector. Fundamental properties such as continuity, nonexpansiveness, and monotonicity are investigated. We also discuss the Yamagishi-Yamada operator. Numerous examples illustrate our results. 
Heinz H. Bauschke, Caifang Wang, Xianfu Wang, Jia Xu
math.OC math.FA math.NA