On the Monotone Variational Inclusion Problems: A New Algorithm-Based Modified Splitting Approach

In this paper, we introduce and analyze an inertial viscosity forward–backward splitting approach. We approximate a common solution of the monotone variational inclusion problem by using the demicontractive mapping in a real Hilbert space. It is shown that the sequence produced by our suggested algorithm has a strong convergence to a solution obtained by other methods. In particular, we obtain the strong convergence when the underlying single-valued operator is Lipschitz, continuous and monotone. We use the new findings to solve a split convex minimization problem and an optimal control problem. We conduct a numerical analysis and provide an example of the proposed algorithm to show that its rate of convergence outperforms results found in the literature.