A refined convergence analysis of Popov's algorithm for pseudo-monotone variational inequalities

In this work, we present a refined convergence analysis of the Popov's projection algorithm for solving pseudo-monotone variational inequalities in Hilbert spaces. Our analysis results in a larger range of stepsize, which is achieved by using a new Lyapunov function. Furthermore, when the operator is strongly pseudo-monotone and Lipschitz continuous, we establish the linear convergence of the sequence generated by the Popov's algorithm. As a by-product of our analysis, we extend the range of stepsize in the projected reflected gradient algorithm for solving unconstrained pseudo-monotone variational inequalities.