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 of the initial iterate to the closest fixed point divided by the number of iterations plus one.

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Year of publication:	2020
Authors:	Lieder, Felix
Published in:	Optimization Letters. - Berlin, Heidelberg : Springer, ISSN 1862-4480. - Vol. 15.2020, 2, p. 405-418
Publisher:	Berlin, Heidelberg : Springer
Subject:	Halpern-iteration \| Fixed point methods \| First order methods \| Semidefinite programming \| Performance estimation \| Proximal point

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Type of publication:	Article
Type of publication (narrower categories):	Article
Language:	English
Other identifiers:	10.1007/s11590-020-01617-9 [DOI]
Source:	EconStor

Persistent link: https://www.econbiz.de/10014504510