  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.
