Bounded perturbation resilience of viscosity proximal algorithm for solving split variational inclusion problems with applications to compressed sensing and image recovery.

Split variational inclusion problems are core and useful technique that connects many important problems in nonlinear analysis. This paper proposes a resolvent‐based superiorization method for solving split variational inclusion problems, and some strong convergence theorems are proved under some mild conditions. Superiorization iterative procedures are simple yet powerful method that interlaces two algorithmic procedures under the assumption that one of the algorithmic procedure called the basic algorithm is resilient to the disturbances of its iterates caused by the activities of the other algorithm called perturbations. The numerical results in this paper show that our results are improvements and extensions of the corresponding results announced by many others. [ABSTRACT FROM AUTHOR]