Three-step approximation methods from continuous and discrete perspective for quasi-variational inequalities

The objective of this manuscript is to study the convergence of three-step approximation methods for quasi-variational inequalities in the general case. First, we propose the three-step dynamical system and carry out an asymptotic analysis for the generated trajectories. The explicit time discretization of this system results into a three-step iterative method, which we prove to converge also when it is applied to strongly-monotone quasi-variational inequalities. In addition, we show that linear convergence is guaranteed under strong-monotonicity.