On Subgradient Projectors
Heinz H. Bauschke, Caifang Wang, Xianfu Wang, Jia Yun Xu · SIAM Journal on Optimization · 2015
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.