In this paper, we discuss the split monotone variational inclusion
problem and propose two new inertial algorithms in infinite-dimensional
Hilbert spaces. As well as, the iterative sequence by the proposed
algorithms converges strongly to the solution of a certain variational
inequality with the help of the hybrid steepest descent method.
Furthermore, an adaptive step size criterion is considered in suggested
algorithms to avoid the difficulty of calculating the operator norm.
Finally, some numerical experiments show that our algorithms are
realistic and summarize the known results.