A forward-reflected-anchored-backward splitting algorithm with double inertial effects for solving non-monotone inclusion problems

In this paper, we investigate inclusion problems involving operators that may not be monotone in the classical sense.Specifically, we consider a generalized notion of monotonicity, allowing the modulus of monotonicity to take negative values.This broader assumption extends the applicability of our results to a wider class of operators.To address these non-monotone inclusion problems, we employ the two-step inertial forward-reflected-anchored-backward splitting algorithm proposed in [I.Chinedu, A. Maggie, O.A. Kazeem, Two-step inertial forward-reflected-anchored-backward splitting algorithm for solving monotone inclusion problems, Comput.Appl.Math.42 (2023), 351] and establish the strong convergence of the generated sequence.Our findings relaxed the assumptions on the operators.We demonstrate the applicability of our approach to various optimization settings, including constrained optimization problems, mixed variational inequalities, and variational inequalities.Finally, we provide a numerical example to illustrate the practical effectiveness of the proposed algorithm.