Montag, 23. April 2018, 16:45 - 17:45 iCal

ISOR Colloquium

"Rates of convergence for the Krasnoselskii-Mann fixed point iteration"

Speaker: Roberto Cominetti (Univ. A. Ibanez, Santiago de Chile)

HS 7 OMP1 (#1.303), 1st floor
Oskar-Morgenstern-Platz 1, 1090 Wien

Vortrag


We analyze the convergence of an inexact version of the classical Krasnoselskii-Mann iteration for computing fixed points of nonexpansive maps in Banach spaces. Our main result establishes a new metric bound for the fixed-point residuals, from which we derive their rate of convergence as well as the convergence of the iterates towards a fixed point. To this end we consider a nested family of optimal transport problems that provide a recursive bound for the distance between the iterates. These recursive bounds are in turn interpreted as expected rewards for an underlying Markov chain, which leads to explicit rates of convergence. In the case of the exact iteration we show that these bounds are tight by building a nonexpansive map that attains them with equality, and we deduce that the optimal constant of asymptotic regularity is exactly $1/\sqrt{\pi}$. The results are extended to continuous time to study the asymptotics of non-autonomous evolution equations governed by nonexpansive operators.

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Veranstalter

Institut für Statistik und Operations Research


Kontakt

Mag. Vera Lehmwald
Fakultät für Wirtschaftswissenschaften
Institut für Statistik und Operations Research
+43 1 4277 38651
vera.lehmwald@univie.ac.at