New accelerated splitting algorithm for monotone inclusion problems

Forward-reflected-backward splitting algorithm with inertial extrapolation of two inertial effects to find a zero of the sum of a maximal monotone and a Lipschitz continuous monotone operator is studied in this paper. The incorporation of two inertial effects on the extrapolation step is to further improve the convergence speed of the forward-reflected-backward splitting algorithm with one inertial effect extrapolation already proposed in the literature. The parameter of the second inertial effect of our proposed algorithm is chosen to be non-positive. Weak, strong, and linear convergence results are obtained under standard conditions in Hilbert spaces. Preliminary numerical illustrations show that our proposed algorithm is competitive with other related algorithms in the literature.