Convergence of Extrapolated Dynamic String-Averaging Cutter Methods and Applications

Convergence of Extrapolated Dynamic String-Averaging Cutter Methods and Applications

Year:    2023

Author:    Nguyen Buong, Nguyen Duong Nguyen

East Asian Journal on Applied Mathematics, Vol. 13 (2023), Iss. 2 : pp. 257–275

Abstract

Two extrapolated dynamic string-averaging cutter methods for finding a common fixed point of a finite family of demiclosed cutters in a Hilbert space are developed. One method converges weakly to a common fixed point of the family. The other converges in norm and is a combination of the method mentioned and the steepest-descent method. The proof of the strong convergence does not employ any additional cutter related conditions such as approximate shrinking and bounded regularity of their fixed point sets often used in literature. Particular cases of the last method and applications to a convex optimization problem over the intersection of the level sets and the LASSO problem with computational experiments are provided as illustrations.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/eajam.2022-177.220922

East Asian Journal on Applied Mathematics, Vol. 13 (2023), Iss. 2 : pp. 257–275

Published online:    2023-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    19

Keywords:    Quasi-nonexpansive mapping fixed point variational inequality steepest-descent method.

Author Details

Nguyen Buong

Nguyen Duong Nguyen

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