The Popov's Algorithm with Optimal Bounded Stepsize for Generalized Monotone Variational Inequalities

Abstract

For solving constrained (pseudo)-monotone variational inequality, we prove that the upper bound of stepsize $\frac{1}{2L}$ established for the Popov's algorithm and the forward-reflected-backward algorithm is tight. For unconstrained case, we can enlarge the upper bound to $\frac{1}{\sqrt{3}L}$ and show that this upper bound is also tight. The convergence analysis is carried out by using a new Lyapunov-type function.