Convergence of proximal splitting algorithms in \(\operatorname{CAT}(\kappa)\) spaces and beyond

DOI10.1186/s13663-021-00698-0OpenAlexW3193922030MaRDI QIDQ2138444

D. Russell Luke, Florian Lauster

Publication date: 12 May 2022

Published in: Fixed Point Theory and Algorithms for Sciences and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13663-021-00698-0

zbMATH Keywords

fixed point iterationnonexpansive mappingsproximal point algorithm\(\operatorname{CAT}(k)\) spaceaveraged mappingsfirmly nonexpansive\(p\)-uniformly convex

Mathematics Subject Classification ID

Fixed-point theorems (47H10) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Geodesics in global differential geometry (53C22) Global Riemannian geometry, including pinching (53C20) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Decomposition methods (49M27) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (2)

Unnamed Item ⋮ \( \alpha \)-firmly nonexpansive operators on metric spaces

Cites Work

• The asymptotic behavior of the composition of firmly nonexpansive mappings
• \( \alpha \)-firmly nonexpansive operators on metric spaces
• Necessary conditions for linear convergence of iterated expansive, set-valued mappings
• Proximal-type algorithms for split minimization problem in P-uniformly convex metric spaces
• Jensen's inequality on convex spaces
• Convexities of metric spaces
• Poincaré inequalities, embeddings, and wild groups
• Local Linear Convergence of the ADMM/Douglas--Rachford Algorithms without Strong Convexity and Application to Statistical Imaging
• Characterizations of Łojasiewicz inequalities: Subgradient flows, talweg, convexity
• Quantitative Convergence Analysis of Iterated Expansive, Set-Valued Mappings
• Implicit Functions and Solution Mappings
• The Łojasiewicz Inequality for Nonsmooth Subanalytic Functions with Applications to Subgradient Dynamical Systems

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