  Qualitative and quantitative aspects for variational inequalities governed by
strongly pseudomonotone operators on Hilbert space are investigated in this
paper. First, we establish a global error bound for the solution set of the
given problem with the residual function being the normal map. Second, we will
prove that the iterative sequences generated by gradient projection method
(GPM) with stepsizes forming a non-summable diminishing sequence of positive
real numbers converge to the unique solution of the problem when the operator
is bounded over the constraint set. Two counter-examples are given to show the
necessity of the boundedness assumption and the variation of stepsizes. We also
analyze the convergence rate of the iterative sequences generated by this
method. Finally, we give an in-depth comparison between our algorithm and a
recent related algorithm through several numerical experiments.
