Strong Convergence for the Alternating Halpern–Mann Iteration in CAT(0) Spaces

DOI10.1137/22m1511199zbMath1519.47080arXiv2112.14525OpenAlexW4380875287MaRDI QIDQ6158004

Pedro Pinto, Bruno Dinis

Publication date: 22 June 2023

Published in: SIAM Journal on Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2112.14525

zbMATH Keywords

strong convergencemetastabilityasymptotic regularity\(\mathrm{CAT}(0)\) spaces

Mathematics Subject Classification ID

Monotone operators and generalizations (47H05) Iterative procedures involving nonlinear operators (47J25) Fixed-point and coincidence theorems (topological aspects) (54H25) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Functionals in proof theory (03F10)

Related Items

A computational study of a class of recursive inequalities

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Effective metastability for modified Halpern iterations in CAT(0) spaces
• On the quantitative asymptotic behavior of strongly nonexpansive mappings in Banach and geodesic spaces
• Strong convergence of modified Halpern iterations in \(\mathrm{CAT}(0)\) spaces
• On quantitative versions of theorems due to F. E. Browder and R. Wittmann
• Effective metastability of Halpern iterates in \(CAT(0)\) spaces
• A quadratic rate of asymptotic regularity for CAT(0)-spaces
• Halpern's iteration in CAT(0) spaces
• Strong convergence of a modified Krasnoselski-Mann iterative algorithm for non-expansive mappings
• Weak convergence theorems for nonexpansive mappings in Banach spaces
• Strong convergence theorems for resolvents of accretive operators in Banach spaces
• Approximation of fixed points of nonexpansive mappings
• Extension problems for accretive sets in Banach spaces
• Projection and proximal point methods: Convergence results and counterexamples.
• Some computational aspects of metric fixed-point theory
• Strong convergence of modified Mann iterations
• Viscosity approximation methods for nonexpansive mappings
• Quantitative results on a Halpern-type proximal point algorithm
• Quantitative translations for viscosity approximation methods in hyperbolic spaces
• Abstract strongly convergent variants of the proximal point algorithm
• On the removal of weak compactness arguments in proof mining
• Quantitative results for Halpern iterations of nonexpansive mappings
• The primes contain arbitrarily long arithmetic progressions
• On \(\Delta\)-convergence theorems in CAT\((0)\) spaces
• Quasilinearization and curvature of Aleksandrov spaces
• Reductive groups over a local field
• A uniform betweenness property in metric spaces and its role in the quantitative analysis of the ``lion-man game
• On modified Halpern and Tikhonov-Mann iterations
• Iteration processes for nonexpansive mappings
• Iterative Algorithms for Nonlinear Operators
• A convexity in metric space and nonexpansive mappings. I.
• On the Numerical Solution of Heat Conduction Problems in Two and Three Space Variables
• Nonexpansive iterations in hyperbolic spaces
• Local stability of ergodic averages
• Computational Problems in Metric Fixed Point Theory and their Weihrauch Degrees
• A quantitative mean ergodic theorem for uniformly convex Banach spaces
• Splitting Algorithms for the Sum of Two Nonlinear Operators
• NON-STRICTLY CONVEX MINIMIZATION OVER THE FIXED POINT SET OF AN ASYMPTOTICALLY SHRINKING NONEXPANSIVE MAPPING
• Inducing strong convergence into the asymptotic behaviour of proximal splitting algorithms in Hilbert spaces
• Regular Sequences of Quasi-Nonexpansive Operators and Their Applications
• Some logical metatheorems with applications in functional analysis
• A Rate of Metastability for the Halpern Type Proximal Point Algorithm
• Quadratic rates of asymptotic regularity for the Tikhonov–Mann iteration
• PROOF-THEORETIC METHODS IN NONLINEAR ANALYSIS
• NONEXPANSIVE NONLINEAR OPERATORS IN A BANACH SPACE
• Norm convergence of multiple ergodic averages for commuting transformations
• Applied Proof Theory: Proof Interpretations and Their Use in Mathematics
• The solution by iteration of nonlinear functional equations in Banach spaces
• Fixed points of nonexpanding maps
• Mean Value Methods in Iteration
• Convex analysis and monotone operator theory in Hilbert spaces

This page was built for publication: Strong Convergence for the Alternating Halpern–Mann Iteration in CAT(0) Spaces