A modified generalized version of projected reflected gradient method in Hilbert spaces

This article is concerned with a universal version of projected reflected gradient method with new step size for solving variational inequality problem in Hilbert spaces. Under appropriate assumptions controlled by the operators and parameters, we acquire the weak convergence of the proposed algorithm. Moreover, we establish an R-linear convergence rate of our method on the condition that the relevant mapping is strongly monotone. We rework our first algorithm so that it can be simplified to several generalized methods in the literature. The efficacy and availability of our proposed iterative scheme are demonstrated in numerical experiments.