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

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. 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.

Joint work with H. Bauschke

optimization and control

Audience: researchers in the topic

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