A SELF ADAPTIVE INERTIAL ALGORITHM FOR SOLVING SPLIT VARIATIONAL INCLUSION AND FIXED POINT PROBLEMS WITH APPLICATIONS

We propose a general iterative scheme with inertial term and self-adaptive stepsize for approximating a common solution of Split Varia-tional Inclusion Problem (SVIP) and Fixed Point Problem (FPP) for a quasi-nonexpansive mapping in real Hilbert spaces. We prove that our iterative scheme converges strongly to a common solution of SVIP and FPP for a quasi-nonexpansive mapping, which is also a solution of a certain optimiza-tion problem related to a strongly positive bounded linear operator. We apply our proposed algorithm to the problem of finding an equilibrium point with minimal cost of production for a model in industrial electricity production. Numerical results are presented to demonstrate the efficiency of our algorithm in comparison with some other existing algorithms in the literature.