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.
@article{arxiv.1403.7135,
title = {On subgradient projectors},
author = {Heinz H. Bauschke and Caifang Wang and Xianfu Wang and Jia Xu},
journal= {arXiv preprint arXiv:1403.7135},
year = {2014}
}