Strong and linear convergence of projection-type method with an inertial term for finding minimum-norm solutions of pseudomonotone variational inequalities in Hilbert spaces

The purpose of this paper is to investigate pseudomonotone variational inequalities in real Hilbert spaces. For solving this problem, we introduce a new method. The proposed algorithm combines the advantages of the subgradient extragradient method and the projection and contraction method. We establish the strong convergence of the proposed algorithm under conditions pseudomonotonicity and Lipschitz continuity assumptions. Moreover, under additional strong pseudomonotonicity and Lipschitz continuity assumptions, the linear convergence of the sequence generated by the proposed algorithm is obtained. Numerical examples provide to illustrate the potential of our algorithms as well as compare their performances to several related results.