Convergence of Extrapolated Dynamic String-Averaging Cutter Methods and Applications

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.