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 - <p style="text-align: justify;">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.</p>