On Subgradient Projectors | Zendy

Heinz H. Bauschke | Zendy; Caifang Wang | Zendy; Xianfu Wang | Zendy; Jia Xu | Zendy

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On Subgradient Projectors

Author(s) -

Heinz H. Bauschke,

Caifang Wang,

Xianfu Wang,

Jia Xu

Publication year - 2015

Publication title -

siam journal on optimization

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.066

H-Index - 136

eISSN - 1095-7189

pISSN - 1052-6234

DOI - 10.1137/14096267x

Subject(s) - subgradient method , mathematics , projection (relational algebra) , convex optimization , regular polygon , monotonic function , projector , operator (biology) , key (lock) , mathematical optimization , computer science , algorithm , artificial intelligence , mathematical analysis , geometry , biochemistry , chemistry , computer security , repressor , transcription factor , gene

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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