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.
Citation
submitted