Roots of the identity operator and proximal mappings: (Classical and phantom) cycles and gap vectors

Bauschke, Heinz; Wang, Xianfu

doi:10.1090/proc/16049

Roots of the identity operator and proximal mappings: (Classical and phantom) cycles and gap vectors
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by Heinz H. Bauschke and Xianfu Wang PDF

Proc. Amer. Math. Soc. 150 (2022), 5383-5395 Request permission

Abstract:

Recently, Simons provided a lemma for a support function of a closed convex set in a general Hilbert space and used it to prove the geometry conjecture on cycles of projections. In this paper, we extend Simons’s lemma to closed convex functions, show its connections to Attouch–Théra duality, and use it to characterize (classical and phantom) cycles and gap vectors of proximal mappings.

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