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New Convergence Results for Inertial Krasnoselskii–Mann Iterations in Hilbert Spaces with Applications

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Abstract

We consider inertial iteration methods for Fermat–Weber location problem and primal–dual three-operator splitting in real Hilbert spaces. To do these, we first obtain weak convergence analysis and nonasymptotic O(1/n) convergence rate of the inertial Krasnoselskii–Mann iteration for fixed point of nonexpansive operators in infinite dimensional real Hilbert spaces under some seemingly easy to implement conditions on the iterative parameters. One of our contributions is that the convergence analysis and rate of convergence results are obtained using conditions which appear not complicated and restrictive as assumed in other previous related results in the literature. We then show that Fermat–Weber location problem and primal–dual three-operator splitting are special cases of fixed point problem of nonexpansive mapping and consequently obtain the convergence analysis of inertial iteration methods for Fermat–Weber location problem and primal–dual three-operator splitting in real Hilbert spaces. Some numerical implementations are drawn from primal–dual three-operator splitting to support the theoretical analysis.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, People’s Republic of China

    Yekini Shehu

  2. Institute of Science and Technology (IST), Am Campus 1, 3400, Klosterneuburg, Austria

    Yekini Shehu

  3. Department of Mathematics and Physical Sciences, California University of Pennsylvania, California, PA, USA

    Olaniyi S. Iyiola

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  1. Olaniyi S. Iyiola
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  2. Yekini Shehu
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The research of this author is supported by the Postdoctoral Fellowship from Institute of Science and Technology (IST), Austria.

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Iyiola, O.S., Shehu, Y. New Convergence Results for Inertial Krasnoselskii–Mann Iterations in Hilbert Spaces with Applications. Results Math 76, 75 (2021). https://doi.org/10.1007/s00025-021-01381-x

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