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Qualitative and quantitative aspects for variational inequalities governed bystrongly pseudomonotone operators on Hilbert space are investigated in thispaper. First, we establish a global error bound for the solution set of thegiven problem with the residual function being the normal map. Second, we willprove that the iterative sequences generated by gradient projection method(GPM) with stepsizes forming a non-summable diminishing sequence of positivereal numbers converge to the unique solution of the problem when the operatoris bounded over the constraint set. Two counter-examples are given to show thenecessity of the boundedness assumption and the variation of stepsizes. We alsoanalyze the convergence rate of the iterative sequences generated by thismethod. Finally, we give an in-depth comparison between our algorithm and arecent related algorithm through several numerical experiments.

Variational Inequalities Governed By Strongly Pseudomonotone Operators