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On the Convergence Rate of the Halpern-Iteration

Felix Lieder (lieder***at***opt.uni-duesseldorf.de)

Abstract: 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, 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. Our proof technique is based on semidefinite programming and duality.

Keywords: Halpern-Iteration, fixed point methods, first order methods, semidefinite programming

Category 1: Linear, Cone and Semidefinite Programming

Category 2: Nonlinear Optimization

Citation: submitted

Download: [PDF]

Entry Submitted: 11/22/2017
Entry Accepted: 11/22/2017
Entry Last Modified: 02/15/2019

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