On the convergence rate of the Halpern-iteration Article Swipe

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Mathematics Hilbert space Rate of convergence Duality (order theory) Bounded function Fixed point Norm (philosophy) Convergence (economics) Semidefinite programming Applied mathematics Computational intelligence Fixed-point iteration Combinatorics Discrete mathematics Mathematical optimization Pure mathematics Mathematical analysis Computer science Economics Channel (broadcasting) Machine learning Political science Economic growth Computer network Law

Felix Lieder ·

YOU? · · 2020 · Open Access · · DOI: https://doi.org/10.1007/s11590-020-01617-9 · OA: W3041776387

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.