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Volume 13, Issue 2
Convergence of Extrapolated Dynamic String-Averaging Cutter Methods and Applications

Nguyen Buong & Nguyen Duong Nguyen

East Asian J. Appl. Math., 13 (2023), pp. 257-275.

Published online: 2023-04

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  • 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.

  • AMS Subject Headings

46N10, 47H09, 47H10, 47J25, 47N10, 65F10, 65J99

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-13-257, author = {Buong , Nguyen and Nguyen , Nguyen Duong}, title = {Convergence of Extrapolated Dynamic String-Averaging Cutter Methods and Applications}, journal = {East Asian Journal on Applied Mathematics}, year = {2023}, volume = {13}, number = {2}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.2022-177.220922}, url = {http://global-sci.org/intro/article_detail/eajam/21648.html} }
TY - JOUR T1 - Convergence of Extrapolated Dynamic String-Averaging Cutter Methods and Applications AU - Buong , Nguyen AU - Nguyen , Nguyen Duong JO - East Asian Journal on Applied Mathematics VL - 2 SP - 257 EP - 275 PY - 2023 DA - 2023/04 SN - 13 DO - http://doi.org/10.4208/eajam.2022-177.220922 UR - https://global-sci.org/intro/article_detail/eajam/21648.html KW - Quasi-nonexpansive mapping, fixed point, variational inequality, steepest-descent method. AB -

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.

Nguyen Buong & Nguyen Duong Nguyen. (2023). Convergence of Extrapolated Dynamic String-Averaging Cutter Methods and Applications. East Asian Journal on Applied Mathematics. 13 (2). 257-275. doi:10.4208/eajam.2022-177.220922
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