  Many recently proposed gradient projection algorithms with inertial
extrapolation step for solving quasi-variational inequalities in Hilbert spaces
are proven to be strongly convergent with no linear rate given when the cost
operator is strongly monotone and Lipschitz continuous. In this paper, our aim
is to design an inertial type gradient projection algorithm for
quasi-variational inequalities and obtain its linear rate of convergence.
Therefore, our results fill in the gap for linear convergence results for
inertial type gradient projection algorithms for quasi variational inequalities
in Hilbert spaces. We perform numerical implementations of our proposed
algorithm and give numerical comparisons with other related inertial type
gradient projection algorithms for quasi variational inequalities in the
literature.
