C-FISTA type projection algorithm for quasi-variational inequalities

In this paper, we first propose a version of FISTA, called C-FISTA type gradient projection algorithm, for quasi-variational inequalities in Hilbert spaces and obtain linear convergence rate. Our results extend the results of Nesterov for C-FISTA algorithm for strongly convex optimization problem and other recent results in the literature where linear convergence results of C-FISTA are obtained for strongly convex composite optimization problems. For a comprehensive study, we also introduce a new version of gradient projection algorithm with momentum terms and give linear rate of convergence. We show the adaptability and effectiveness of our proposed algorithms through numerical comparisons with other related gradient projection algorithms that are in the literature for quasi-variational inequalities.