Adaptive inertial subgradient extragradient methods for finding minimum-norm solutions of pseudomonotone variational inequalities

Abstract

In this paper, four modified inertial subgradient extragradient methods with a new non-monotonic step size criterion are investigated for pseudomonotone variational inequality problems in real Hilbert spaces. Our algorithms employ two different step sizes in each iteration to update the values of iterative sequences, and they work well without the prior information about the Lipschitz constant of the operator. Strong convergence theorems of the proposed iterative schemes are established under some suitable and mild conditions. Some numerical examples are provided to demonstrate the computational efficiency and advantages of the proposed methods over other known ones.