Strong convergence of inertial extragradient methods for solving pseudomonotone variational inequality problems

The extragradient method is an efficient approach for solving variational inequality problems. In this paper, we propose two kinds of inertial viscosity extragradient methods with new step sizes for tackling variational inequality problems characterized by pseudomonotone and Lipschitz continuous cost operator in real Hilbert spaces. Notably, these algorithms necessitate the computation of just a single projection onto the feasible set, and the introduced step sizes exhibit a nonincreasing pattern while being independent of the Lipschitz constant of the cost operator. Strong convergence theorems of the presented algorithms are established under some conditions. Numerical experiments are conducted to demonstrate the efficiency and reliability of our algorithms.