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.
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