Linear rates of asymptotic regularity for Halpern-type iterations
Hora\c{t}iu Cheval, Lauren\c{t}iu Leu\c{s}tean
TL;DR
This paper derives explicit linear convergence rates for Halpern-type iterative methods in nonlinear analysis using a lemma by Sabach and Shtern.
Contribution
It provides the first explicit linear rates of asymptotic regularity for Halpern-type iterations in optimization and nonlinear analysis.
Findings
Established linear convergence rates for Halpern-type iterations
Applied Sabach and Shtern's lemma to analyze convergence
Enhanced understanding of convergence behavior in nonlinear iterative methods
Abstract
In this note we apply a lemma due to Sabach and Shtern to compute linear rates of asymptotic regularity for Halpern-type nonlinear iterations studied in optimization and nonlinear analysis.
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Taxonomy
TopicsOptimization and Variational Analysis · Advanced Optimization Algorithms Research · Matrix Theory and Algorithms