Scaled forward-backward algorithm and the modified superiorized version for solving the split monotone variational inclusion problem
Optimization Eruditorum, Volume 1, Issue 1, June 2024, Pages 56–74
MINGXIA ZHENG
College of Science, Civil Aviation University of China, Tianjin 300300, China
YANNI GUO
College of Science, Civil Aviation University of China, Tianjin 300300, China
Abstract
In this paper, we propose an inexact scaled forward-backward algorithm to solve the split monotone variational inclusion problem in a real Hilbert space and prove the strong convergence of it under appropriate conditions. Based on this, we discuss the bounded perturbation resilience of the exact algorithm for introducing the corresponding superiorized version and the superiorization algorithm with restarted perturbations. The numerical experiments illustrate that the proposed algorithms perform well and the superiorization version with restarted perturbations has advantage in decreasing the number of the iterations.
Cite this Article as
Mingxia Zheng and Yanni Guo, Scaled forward-backward algorithm and the modified superiorized version for solving the split monotone variational inclusion problem, Optimization Eruditorum, 1 (2024), 56–74