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New inertial factors of the Krasnoselskii-Mann iteration

Dong Yunda(ydong***at***zzu.edu.cn)

Abstract: In this article, we consider the Krasnosel'ski\u{\i}-Mann iteration for approximating a fixed point of any given non-expansive operator in real Hilbert spaces, and we study an inertial version proposed by Maing\'{e} recently. As a result, we suggest new conditions on the inertial factors to ensure weak convergence. They are free of iterates and depend on the original coefficient of the Krasnosel'ski\u{\i}-Mann iteration. In particular, in a special case that corresponds to the Douglas-Rachford splitting, the upper bound of the sequence of inertial factors is merely required to strictly less than $1/3$. Rudimentary numerical results indicate practical usefulness of our suggested conditions.

Keywords: Non-expansive operator; fixed point; Krasnoselskii-Mann iteration; inertial factor; the Douglas-Rachford splitting

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )


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Entry Submitted: 05/05/2019
Entry Accepted: 05/05/2019
Entry Last Modified: 05/05/2019

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