An inertial extragradient algorithm with non-monotone step sizes for variational inequality problems and fixed point problems of nonexpansive semigroups

In this paper, we propose an inertial extragradient algorithm with non-monotone step sizes for approximating a common solution of a variational inequality problem of pseudomonotone and uniformly continuous operators and a fixed point problem of nonexpansive semigroups in the setting of real Hilbert spaces.By utilizing a self-adaptive technique that produces non-monotonic step sizes, our method ensures strong convergence without requiring Armijo-type line searches.Finally, to assess the performance of the proposed algorithm, we provide some numerical results.