SELF-ADAPTIVE INERTIAL SHRINKING PROJECTION ALGORITHMS FOR SOLVING PSEUDOMONOTONE VARIATIONAL INEQUALITIES

Abstract

In this paper, we construct two fast iterative methods to solve pseudomonotone variational inequalities in real Hilbert spaces. The advantage of the suggested iterative schemes is that they can adaptively update the iterative step size through some previously known information without performing any line search process. Strong convergence theorems of the proposed algorithms are established under some relaxed conditions imposed on the parameters. Finally, several numerical tests are given to show the advantages and efficiency of the proposed approaches compared with the existing results.