New inertial modification of regularized algorithms for solving split variational inclusion problem

In this paper, we introduce two new self-adaptive iterative algorithms for finding the solution of a split variational inclusion problem in real Hilbert spaces. The strong convergence theorems are proved under suitable conditions. In applications, the main results are applied for solving the split feasibility problem, the split minimization problem, and the split common fixed point problem. In order to test the numerical performances, the proposed algorithms are compared with several existing algorithms in the literature. Finally, the computational experiments show that the proposed algorithms are fast and more efficient than other approaches. (c) 2023 Elsevier B.V. All rights reserved.

Automated summary

This paper introduces two new self-adaptive iterative algorithms for solving split variational inclusion problems in real Hilbert spaces, and proves their strong convergence. The algorithms are applied to solve various practical problems and are shown to be effective and efficient through computational experiments.