On the convergence rate of the Halpern-iteration

In this work, we give a tight estimate of the rate of convergence for the Halpern-iteration for approximating a fixed point of a nonexpansive mapping in a Hilbert space. Specifically, using semidefinite programming and duality we prove that the norm of the residuals is upper bounded by the distance...

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Bibliographic Details
Published inOptimization letters Vol. 15; no. 2; pp. 405 - 418
Main Author Lieder, Felix
Format Journal Article
LanguageEnglish
Published Berlin, Heidelberg Springer 01.03.2021
Springer Berlin Heidelberg
Subjects
Computational Intelligence
First order methods
Fixed point methods
Halpern-iteration
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Operations Research/Decision Theory
Optimization
Performance estimation
Proximal point
Semidefinite programming
Simulation
Halpern-iteration
Semidefinite programming
First order methods
Proximal point
Performance estimation
Fixed point methods
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Summary:In this work, we give a tight estimate of the rate of convergence for the Halpern-iteration for approximating a fixed point of a nonexpansive mapping in a Hilbert space. Specifically, using semidefinite programming and duality we prove that the norm of the residuals is upper bounded by the distance of the initial iterate to the closest fixed point divided by the number of iterations plus one.
ISSN:1862-4480
1862-4472
1862-4480
DOI:10.1007/s11590-020-01617-9