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On subgradient projectors (1403.7135v1)
Published 27 Mar 2014 in math.OC, math.FA, and math.NA
Abstract: 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.
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