General Inertial Mann Algorithms and Their Convergence Analysis for Nonexpansive Mappings

Qiao-Li Dong (), Yeol Je Cho () and Themistocles M. Rassias ()
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Qiao-Li Dong: College of Science, Civil Aviation University of China
Yeol Je Cho: Gyeongsang National University
Themistocles M. Rassias: National Technical University of Athens

A chapter in Applications of Nonlinear Analysis, 2018, pp 175-191 from Springer

Abstract: Abstract In this article, we introduce general inertial Mann algorithms for finding fixed points of nonexpansive mappings in Hilbert spaces, which includes some other algorithms as special cases. We reanalyze the accelerated Mann algorithm, which actually is an inertial type Mann algorithm. We investigate the convergence of the general inertial Mann algorithm, based on which, the strict convergence condition on the accelerated Mann algorithm is eliminated. Also, we apply the general inertial Mann algorithm to show the existence of solutions of the minimization problems by proposing a general inertial type gradient-projection algorithm. Finally, we give preliminary experiments to illustrate the advantage of the accelerated Mann algorithm.

Keywords: Mann Algorithm; General Inertia; Nonexpansive Mappings; Inertial Type; Gradient Projection Algorithm (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-89815-5_7

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DOI: 10.1007/978-3-319-89815-5_7

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