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

DOI10.1090/proc/16049OpenAlexW4214845636WikidataQ114094163 ScholiaQ114094163MaRDI QIDQ5039260

Heinz H. Bauschke, Shawn Xianfu Wang

Publication date: 12 October 2022

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2201.05189

zbMATH Keywords

cycleconvex functionAttouch-Théra dualityFenchel conjugategap vectorphantom cyclephantom gap vectorroot of identity operatorSimons's lemmatranslation-invariant function

Mathematics Subject Classification ID

Convex programming (90C25) Monotone operators and generalizations (47H05) Set-valued and variational analysis (49J53) Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) (46C05) Fixed-point theorems (47H10) Convex functions and convex programs in convex geometry (52A41)

Cites Work

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• Resolvents and Yosida approximations of displacement mappings of isometries
• The difference vectors for convex sets and a resolution of the geometry conjecture
• From Hahn--Banach to monotonicity
• Fitzpatrick Functions and Continuous Linear Monotone Operators
• Attouch--Théra Duality, Generalized Cycles, and Gap Vectors
• On the Maximality of Sums of Nonlinear Monotone Operators
• Monotone Linear Relations: Maximality and Fitzpatrick Functions
• Convex analysis and monotone operator theory in Hilbert spaces

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