Full Text: PDF
Received May 15, 2022; Accepted June 19, 2022; Published July 29, 2022
Abstract In recent years, the Douglas-Rachford algorithm has received much attention due to its various applications in image recovery, signal processing, and machine learning. In this paper, we introduce the Mann iteration of Douglas-Rachford algorithm with a new error sequence in Hilbert spaces, and establish its weak convergence under some mild conditions. Furthermore, we propose the Halpern iteration of Douglas-Rachford algorithm with two different error sequences, and prove their strong convergence under some proper conditions. Finally, a feasibility problem is also considered.
How to Cite this Article:
Y. Wang, F. Wang, The Douglas-Rachford algorithm with new error sequences for an inclusion problem, J. Nonlinear Funct. Anal. 2022 (2022) 31.